assignment listening exercise 2.1 hearing meters

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Chapter 4 Communication Skills

4.1 Active Listening

Being a good communicator involves not only being good at speaking. Listening is an essential part of communication and is often the weakest link in the communication process. People usually love to be heard but are often not as excited about listening. Active listening is being engaged as a listener, not just hearing the words.

Are you a good listener? Most of us like to think we are, but when we really think about it, we recognize that we are often only half-listening. We’re distracted, thinking about other things, or formulating what we are going to say in reaction to what we are hearing before the speaker has even finished. Effective listening is one of the most important learning tools you can have in college or university. And it is a skill that will benefit you on the job and help your relationships with others. Listening is nothing more than purposefully focusing on what a speaker is saying with the objective of understanding.

This definition is straightforward, but there are some important concepts that deserve a closer look. “Purposefully focusing” implies that you are actively processing what the speaker is saying, not just letting the sounds of their voice register in your senses. “With the objective of understanding” means that you will learn enough about what the speaker is saying to be able to form your own thoughts about the speaker’s message. Listening is an active process, as opposed to hearing, which is passive.

Being an active listener takes concentration and work. The principles of active listening are not hard to understand, but they are hard to implement and require practice to use them effectively.

Principles of Active Listening

• Focus on what is being said. Give the speaker your undivided attention. Clear your mind of anything else. Don’t prejudge. You want to understand what the person is saying; you don’t need to agree with it.
• Repeat what you just heard. Confirm with the speaker that what you heard is what they said.
• Ask the speaker to expand or clarify. If you are unsure whether or not you understand, ask questions; don’t assume.
• Look for nonverbal signals as well as the words used. Nonverbal messages come from facial expressions, body positioning, arm gestures, and tone of voice. Confirm these body language messages just as you would verbal messages by saying, for example, “You seem very excited about this idea.”
• Listen for requests. A speaker will often hide a request as a statement of a problem. If a friend says, “I hate math!” this may mean, “Can you help me figure out a solution to this problem?”

Exercise: Listening with Your Whole Body

Make two lists.

Think of a person you consider an excellent listener. Picture that person clearly in your mind. Focus on what they do, not what they are saying. Describe what actions and postures they use to show they are listening. Use these items to create your first list.

Think of a person you consider a poor listener. Picture that person clearly in your mind. Focus on what they do, not what they are saying. Describe what actions and postures they use to show they are not listening. Use these items to create your second list.

Now compare these lists with your own behaviour. How many of the body language signals from each side do you think you exhibit? How can you add more of the attitudes and actions in the first list to your own behaviours? How can you control those behaviours you recognize in yourself from the second list?

Active listening should accomplish two things:

• Listening for understanding (i.e. the listener fully understands the speaker.)
• Conveying to the speaker that you are really listening (i.e. the speaker feels understood.)

Active listening involves the following:

• Waiting for the speaker to finish speaking before responding; don’t interrupt.
• Asking questions and asking for clarification about what the speaker is saying.
• Reiterating in your own words what you think they meant in order to clarify meaning and understand intentions.
• Paying attention to body language, gestures, and tone of voice.
• Focusing and giving undivided attention; avoid distractions.
• Showing sensitivity to the speaker’s point of view.
• Being attentive to the speaker, which is demonstrated through eye contact, body language, and facial expressions.

For example, leaning in toward a speaker shows interest in what the speaker is saying, as opposed to leaning away and crossing arms. Crossing arms can be interpreted as rejection of the message (though this can be confusing as sometimes it may just mean the listener is feeling cold). Smiling and nodding indicates that you are following what the speaker is saying and that you are interested to hear more.

Even if the listener doesn’t agree with the speaker, it is important to acknowledge that the speaker has a right to their point of view, their ideas and their feelings. Be respectful of others’ opinions, and keep in mind that cultural differences can impact beliefs, values, and communication styles. Signs of distraction include looking away, humming, doodling, checking your phone, texting, or surfing the web. This communicates that you are uninterested in what the speaker is saying.

Meaningful conversations can’t happen if one side is not listening effectively. The following are some examples of responses that stimulate meaningful understanding.

• I haven’t looked at it like that before…
• That’s a great point…
• Can you tell me more about…?
• It appears that you…
• I get the feeling that you…
• I can see you feel quite strongly about this…
• I can imagine how upsetting (frustrating/hard/emotional) that must have been…
• So what I think you’re saying is…
• Tell me if I’m understanding what you mean. I think you’re ultimately saying that…
• So you mean that…
• Well that seems a bit over the top.
• That’s ridiculous.
• I think you are over-reacting.
• That seems pretty judge-y.

Comments like these put the speaker in a defensive mode. They can be insulting and can inhibit further discussion.

In general, you want to encourage speakers to be able to openly share their message. The more strategies that you use for active listening, the more the speaker will be able to freely share the message, and the more likely you are to be able to truly understand the message. After all, isn’t that the making of good communication?

These strategies are not only useful in one-on-one conversations; they are also useful in educational settings such as listening to lectures in class, listening to lab assistants and fellow students in lab activities, and listening in group work projects. Even in a lecture, if you are busy playing with your phone, or checking your email, you not only convey to the speaker that you are not interested, but you are also distracted from clearly hearing the message. People think that they can multi-task, but in reality they are missing a lot of the message when they are busy doing other things. Furthermore, if you try to look interested, you likely will be more interested. If you sit attentively, you likely will be more attentive.  Practice active listening skills in your various classes and educational activities.

Listening in a classroom or lecture hall to learn can be challenging because you are limited by how—and how much—you can interact with an instructor during the class. The following strategies help make listening at lectures more effective and learning more fun.

• Get your mind in the right space. Prepare yourself mentally to receive the information the speaker is presenting by following the previous prep questions and by doing your assignments (instructors build upon work presented earlier). Being prepared for class will help you listen more actively.
• Get yourself in the right space. Sit toward the front of the room where you can make eye contact with the instructor easily. It will also help to have less distractions to focus on active listening. As an added bonus, instructors often believe students who sit near the front of the room take their subject more seriously and consequently they are more willing to give these students help when needed or to give them the benefit of the doubt when making a judgment call while assigning grades.
• Focus on what is being said. Eliminate distractions. Turn your cell phone off and pack it away in your backpack. If you are using your laptop for notes, close all applications except the one that you use to take notes. Clear your mind and keep quiet. Listen for new ideas. Think like an investigative reporter: you don’t just want to accept what is being said passively—you want to question the material and be convinced that it makes sense.
• Look for signals. Each instructor has a different way of telling you what is important. Some will repeat or paraphrase an idea; others will raise (or lower) their voices; still others will write related words on the board. Learn what signals your instructors tend to use and be on the lookout for them. When they use that tactic, the idea they are presenting needs to go in your notes and in your mind—and don’t be surprised if it appears on a test or quiz!
• Listen for what is not being said. If an instructor doesn’t cover a subject, or covers it only minimally, this signals that that material is not as important as other ideas covered in greater length.

A note about recording lectures: You may want to record a lecture to double-check what you heard in class, but do it with caution.  If you know you are recording the lecture, it may lead you to listen less effectively and think less actively. Additionally, some instructors do not allow students to record their lectures. At any rate, if you record lectures, listen actively the first time, and then use the recording for review, further clarification, and deeper understanding.

Dealing with Special Listening Challenges

What to do if…

• Your instructor speaks too fast. Crank up your preparation. The more you know about the subject, the more you’ll be able to pick up from the instructor. Exchange class notes with other students to fill in gaps in notes. Visit the instructor during office hours to clarify areas you may have missed. You might ask the instructor—very politely, of course—to slow down, but habits like speaking fast are hard to break!
• Your instructor has a heavy accent. Sit as close to the instructor as possible. Make connections between what the instructor seems to be saying and what they are presenting on the board or screen. Ask questions when you don’t understand. Visit the instructor during office hours; the more you speak with the instructor the more likely you will learn to understand the accent.
• Your instructor speaks softly or mumbles. Sit as close to the instructor as possible, and try to hold eye contact as much as possible. Check with other students if they are having problems listening, too; if so, you may want to bring the issue up with the instructor. It may be that the instructor is not used to the lecture hall your class is held in and can easily make adjustments.

Exercise: Active Listening Responses

Choose the correct answer for each question.

• interrupting the speaker to find out more information
• giving the speaker undivided attention
• making occasional eye contact with the speaker while you are multi-tasking
• lounging back to stay comfortable while listening
• I strongly disagree…
• I understand why you might feel that way, but have you considered…
• Wow, that reminds me of the time that…
• I don’t get it.

Exercise: Listening Treasures

Watch this TED Talks video clip and use your active listening skills to truly hear his message. Then answer the following questions.

• What 3 types of listening does the speaker discuss?
• How and why have we been “losing our ability to listen,” as the speaker suggests? He cites 5 ways.
• What are the 5 tools we can use to listen better?

Video: “5 ways to listen better | Julian Treasure” (length 7:42)

Exercise: Active Listening Practise and Analysis

Practise your active listening skills this week. Then report on a situation that happened. Briefly describe the situation, and then describe which active listening skills you used and how effective they were. In hindsight, were there any others which maybe should have been used as well? Did you resort to using ineffective communication skills from habit? Note you will be marked on your ability to recognize and analyze the use of active listening skills (not on how well you did in the situation).

Your assignment should be approximately half to a full typed page double-spaced.

Text Attributions

This chapter includes content adapted from the following sources:

• “Communication Skills” in the Education and Career Planning Open Course by Mary Shier. CC BY .
• “ Are you really listening ” in University Success by N. Mahoney, B. Klassen, and M. D’Eon. Adapted by Mary Shier. CC BY-NC-SA .

Video Attributions

• “ Five ways to listen better ” by Julian Treasure, TEDGlobal 2011. CC BY-NC-SA .

Media Attributions

• USDA/HACU Interns © U.S. Department of Agriculture is licensed under a CC BY-SA (Attribution ShareAlike) license
• Active Listening © Gordon Shier is licensed under a CC BY (Attribution) license

Student Success Copyright © 2020 by Mary Shier is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Music for Ear Training Digital Media and Workbook       Michael Horvit, Timothy Koozin, and Robert Nelson      online drills and streaming audio

Unit 2. Simple Meters

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2: Part II- Hearing Harmony

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• Page ID 55755

• Anthony Brandt & Robert McClure
• Rice University via OpenStax CNX
• 2.1: Hearing Harmony- What is Harmony?
• 2.2: Harmony in Western Music
• 2.3: Expressing Harmony
• 2.4: Listening Gallery- Expressing Harmony
• 2.5: Harmonic Rhythm
• 2.6: Listening Gallery- Harmonic Rhythm
• 2.7: Cadences
• 2.8: Listening Gallery- Cadences
• 2.9: The Tonic
• 2.10: Circular and Linear Progressions
• 2.11: Listening Gallery- Circular and Linear Progressions
• 2.12: The Major-minor Contrast
• 2.13: Modes and Scales
• 2.14: Hearing the Mode
• 2.15: Listening Gallery- Hearing the Mode
• 2.16: Tonic, Mode and Key
• 2.17: Listening Gallery- Tonic, Mode and Key
• 2.18: Music Within a Key
• 2.19: Listening Gallery- Music Within a Key
• 2.20: Postponed Closure
• 2.21: Listening Gallery- Postponing Closure
• 2.22: Chromaticism
• 2.23: Listening Gallery- Chromaticism
• 2.24: Dissonance
• 2.25: Leaving the Key
• 2.26: Harmonic Distance
• 2.27: Modulation
• 2.28: Harmonic Goals
• 2.29: The Return to the Tonic
• 2.30: Final Closure
• 2.31: Listening Gallery- Final Closure
• 2.32: Reharmonizing a Melody
• 2.33: Listening Gallery- Reharmonizing a Melody
• 2.34: Conclusion

1.2 Basics of Meter: Tutorial

Can you tap along to a beat when listening to music? Most music has a pulse, which is a regularly recurring feeling of stress. Meter organizes these pulses into a recurring pattern of strong and weak beats. Each bar will have the same number of beats, unless otherwise indicated with a meter change.

Rhythms in music are the patterns of rhythmic values that exist within the meter. Meter and rhythm do not measure time, like the seconds of a clock, they measure the way notes relate to one another in terms of length.

Naming Meters and Using Bar Lines

Meters have a two-part name that includes the type of beat division followed by the number of beat groupings.

If a meter has a main beat that divides into 2 equal divisions, we call it a simple meter . For example, if the quarter note was equal to 1 beat, that beat would divide into 2 eighth notes and would be a simple meter.

If a meter has a main beat that divides into 3 equal divisions, we call it a compound meter . If a meter had a dotted quarter note as the beat, it would divide into 3 eighth notes and would be a compound meter.

Meters are most often grouped by pulses into 2 beats, 3 beats, or 4 beats. If a meter has 2 beats per bar, we call it a duple meter . If it has 3 beats per bar we call it a triple meter , and if it has 4 beats per bar, we call it a quadruple meter . Beat groupings in music are shown using bar lines, which separate music into bars, also called measures. Bar lines extend from line 1 to line 5 of the staff, and a double bar line signifies the end of a piece.

When naming a meter with its two-part name, we say it is either simple or compound, and either a duple, triple, and quadruple meter. Knowing if a meter is duple, triple, or compound tells us how to conduct it, and how it sounds. Examples of meters can include simple duple, compound duple, simple triple, compound triple, simple quadruple, and compound quadruple.

Meter Signatures

While terms like simple duple are more general terms that can refer to multiple meters, a meter signature, also known as time signature, tell us what specific meter is being used. A meter signature is found right after both the clef and key signature at the start of a piece of music. It consists of two notes stacked on top of each other on the staff. While a meter signature bears some resemblance to a fraction, there is no line drawn between the two numbers in a meter signature. To understand what the two numbers in a meter signature mean, we have to determine whether the meter is a simple meter or a compound meter.

Simple Meters

A simple meter has a main beat that divides into two equal divisions. In a simple meter, the top number in the meter signature tells us how many beats are in the bar. A duple meter will have 2 as the top number and will have 2 beats per bar. A triple meter will have 3 as the top number and 3 beats per bar. A quadruple meter will have 4 as the top number and 4 beats per bar.

The bottom number of the time signature tells us what type of note equals 1 beat. If the bottom number is a 4, the quarter note equals 1 beat. If the bottom number is a 2, the half note equals 1 beat. If the bottom number is an 8, the eighth note equals 1 beat. If the bottom number is a 16, the sixteenth note equals 1 beat. The chart below shows different types of simple meters and their key signatures.

Most often, simple meters will have top numbers with 2, 3, or 4, which can help to quickly identify them.

Compound Meters

A compound meter has a main beat that divides into 3 equal divisions. Meter signature numbers work differently for compound meters than for simple meters. In a compound meter, the top number is the number of divisions of the beat that are in 1 bar. In order to find the number of beats per bar, you divide that top number by 3 because each beat is divided into 3 notes. If the top number is a 6, you divide 6 by 3 and get 2. So, a 6 as the top number is a duple meter with 2 beats per bar. If the top number is a 9, it is a triple meter with 3 beats per bar. If the top number is a 12, it is a quadruple meter with 4 beats per bar.

The bottom number of a compound meter signature in also differs from simple meter. The bottom number in a compound meter signature tells you what type of note equals 1 beat division. In order to find the note that equals 1 beat, you have to remember that you have 3 beat divisions per beat, and add 3 of the type of note indicated together. So, if the bottom number is an 8, you add 3 eighth notes together to find that the beat is equal to 1 dotted quarter note. If the bottom number is a 4, you add 3 quarter notes to get a beat of a dotted half note. If the bottom number is 16, you add 3 sixteenth notes to get a dotted eighth note as the beat. The chart below shows different types of compound meters and their key signatures.

Identifying Meter Signatures

While both simple and compound meters can use the same numbers for the bottom number in the meter signature, the top number can help you quickly identify if a meter is simple or compound. Most often, simple meters will use 2, 3, or 4 as the top numbers. Compound meters most often use 6, 9, or 12 as the top numbers. Looking at the way the rhythms are beamed in the bar can also help you identify which meter is being used, and will be explored further in the chapter on beaming.

Accent Scheme in Meter

As we know from our definition of meter, meter organizes the regularly recurring pulses in music into a recurring pattern of strong and weak beats. One measure or bar in music equals one complete cycle through the pattern of beats. Music that has 2 pulses is called duple meter. In duple meter, the downbeat, or first beat of the bar is the strongest, and the second beat is weaker. In a quadruple meter, there are 4 beats in the bar. The downbeat is the strongest beat, followed by a weak second beat, the third beat is strong (but not the strongest), and the fourth beat is weakest. Notice that all four beats have a different accent strength. In triple meter, there are 3 beats. The downbeat is the strongest, beat 2 is weak, and beat 3 is the weakest beat. Understanding accent scheme can help us to hear whether a piece is in duple, triple, or quadruple meter. Other factors combined with meter, like phrasing and harmony, can also help us distinguish between meters. Listen to the following examples to hear the meter.

simple quadruple or simple duple

simple triple

compound duple or compound quadruple

compound triple

To dive more into how meter plays an integral part in music, look at the music you are currently working on, or would like to learn more about, and think about the following questions:

• Can you hear the accent scheme for the meter signature?
• Why do you think the composer chose that specific meter? What kind of feelings does that meter signature invoke that might change if a different meter signature were used?
• Look at other pieces in the same meter. What elements highlighted by the meter are similar and different to your original piece? Do they have a similar feel?
• Is the piece written for a certain purpose that traditionally uses a specific type of meter (like a dance)?
• What would be different and how would the music sound and look different if they had chosen to use a different beat level or a different number of beats (like in 2 beats instead of 4 beats)?
• What would be different, and how would the music sound and look different if the composer had chosen to use a different subdivision (like compound meter instead of simple meter)?

Comprehensive Musicianship, A Practical Resource Copyright © 2023 by Randall Harlow; Heather Peyton; Jonathan Schwabe; and Daniel Swilley is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Open Resources for English Language Teaching (ORELT) Portal

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You are here, unit 1: listening for pronunciation practice, introduction.

In this first unit of the module on listening, we will illustrate a few activities that you can use in your classroom to improve your students’ listening comprehension by making them understand differences in pronunciation. As an English teacher, you might already be familiar with the phonetic symbols for sounds in English. If you are not, you can refer to any good English dictionary (e.g., Oxford/Cambridge/Longman’s Advanced Learners’ dictionaries) that contains a pronunciation key. This will help you become familiar with phonological information about English sounds, which in turn will enable you to devise classroom activities to develop your students’ listening skills. As you are perhaps aware, the pronunciation of English words differs according to which part of the word is stressed, which vowel is long or short, which words in a sentence are pronounced in their weak forms and so on. To be able to understand and respond appropriately to spoken English, JSS students need to be aware of such distinctions when they hear English being spoken. The activities in this unit will focus on giving students opportunities to hear pronunciation differences in appropriate contexts, so that they can use these skills for real-life listening. At this level, we strongly recommend that you do not teach your students the phonological symbols, because this kind of technical knowledge will not help them in actual communication situations. Instead, you can use your technical knowledge to design pronunciation tasks for classroom practice.

Unit outcomes

Upon completion of this unit you will be able to:

Terminology

Teacher support information.

You might know teachers who do not think there is any need to teach listening skills. This is unfortunate because people actually engage in more listening activities than they engage in reading for the purpose of extracting, understanding and evaluating information. Listening skills will develop only when students have an opportunity to hear English being spoken in natural contexts. Because a child’s home environment may not offer such a context, it is important to include classroom activities where students can listen to samples of oral English that represent or recreate real-life uses of English. In the Resource sections, listening passages are provided for you to read in a normal conversational style or to play on an audio or video player.

Activity 1: Distinguishing sound differences

Activity 2: recognising differences in word stress, activity 3: recognising the use of weak forms.

Have a class discussion on how these contracted forms are the written versions of the weak forms of the verbs, and how people use these weak forms in informal conversations. If the students are to easily understand what people say in conversations, they must become familiar with this special feature of spoken English.

For the activity, tell your students that they will listen to a conversation ( Resource 3a ) twice. The first time they will just have to listen with attention. The second time, they will have to fill in the blanks in the passage ( Resource 3b ) with the full forms of the words that they hear.

To give your students more practice, you can put them in groups of four (i.e., to make two pairs). The first pair will prepare a dialogue similar to the one in Resource 3a , and have a conversation. The other pair will have to write down the words that are said in their weak forms. The pairs then repeat the activity; the second pair writes their dialogue, and the first pair completes the task.

Unit summary

Reflections, resource 1: pat and the sheep on noah’s ship.

“Mummy, Mummy, wake up!” shouted Patricia.

Sally yawned and stretched. “Will this child ever sleep?” she thought. Suddenly she heard a thud. “Oh, no!” thought Sally, “Pat must have slipped again!” “Mummy!” she heard the child scream. Her eyes flew open to see milk poured all over the bed. Her daughter was trying to fill the spilt milk back into the bottle. Sally bit her tongue to stop herself from shouting. “I think I’m going to beat her up now!” muttered Sally to herself. But before she could say anything, Pat ran straight into Sally’s arms. Sally noticed that her daughter had a cut on her upper lip. Sally leaped off the bed quickly and ran down to the bathroom to get some antiseptic. She returned to find Pat standing beside her bed looking at her. In one hand she held her broken milk bottle and in the other she carried a storybook. Sally suddenly realised why her daughter had come to her. It was 7.00 a.m. “Mummy, please tell me the story of the black sheep on Noah’s ship!” she pleaded. Sally laughed. How easily the child had forgotten about her fall and her hunger! Sally quickly peeled a banana, fed it to Pat and popped a headache pill in her own mouth. “She really is a sweet and clever child,” thought Sally. She must remember to tell her husband about this morning’s events!

Resource 2a: Allen’s announcement (transcript)

Resource 2b: allen’s announcement (worksheet), resource 3a: practising weak forms (transcript), resource 3b: practising weak forms (worksheet), teacher question and answer.

17.3 Sound Intensity and Sound Level

Learning objectives.

By the end of this section, you will be able to:

• Define intensity, sound intensity, and sound pressure level.
• Calculate sound intensity levels in decibels (dB).

In a quiet forest, you can sometimes hear a single leaf fall to the ground. After settling into bed, you may hear your blood pulsing through your ears. But when a passing motorist has his stereo turned up, you cannot even hear what the person next to you in your car is saying. We are all very familiar with the loudness of sounds and aware that they are related to how energetically the source is vibrating. In cartoons depicting a screaming person (or an animal making a loud noise), the cartoonist often shows an open mouth with a vibrating uvula, the hanging tissue at the back of the mouth, to suggest a loud sound coming from the throat Figure 17.12 . High noise exposure is hazardous to hearing, and it is common for musicians to have hearing losses that are sufficiently severe that they interfere with the musicians’ abilities to perform. The relevant physical quantity is sound intensity, a concept that is valid for all sounds whether or not they are in the audible range.

Intensity is defined to be the power per unit area carried by a wave. Power is the rate at which energy is transferred by the wave. In equation form, intensity I I is

where P P is the power through an area A A . The SI unit for I I is W/m 2 W/m 2 . The intensity of a sound wave is related to its amplitude squared by the following relationship:

Here Δ p Δ p is the pressure variation or pressure amplitude (half the difference between the maximum and minimum pressure in the sound wave) in units of pascals (Pa) or N/m 2 N/m 2 . (We are using a lower case p p for pressure to distinguish it from power, denoted by P P above.) The energy (as kinetic energy mv 2 2 mv 2 2 ) of an oscillating element of air due to a traveling sound wave is proportional to its amplitude squared. In this equation, ρ ρ is the density of the material in which the sound wave travels, in units of kg/m 3 kg/m 3 , and v w v w is the speed of sound in the medium, in units of m/s. The pressure variation is proportional to the amplitude of the oscillation, and so I I varies as ( Δ p ) 2 ( Δ p ) 2 ( Figure 17.12 ). This relationship is consistent with the fact that the sound wave is produced by some vibration; the greater its pressure amplitude, the more the air is compressed in the sound it creates.

Sound intensity levels are quoted in decibels (dB) much more often than sound intensities in watts per meter squared. Decibels are the unit of choice in the scientific literature as well as in the popular media. The reasons for this choice of units are related to how we perceive sounds. How our ears perceive sound can be more accurately described by the logarithm of the intensity rather than directly to the intensity. The sound intensity level β β in decibels of a sound having an intensity I I in watts per meter squared is defined to be

where I 0 = 10 –12 W/m 2 I 0 = 10 –12 W/m 2 is a reference intensity. In particular, I 0 I 0 is the lowest or threshold intensity of sound a person with normal hearing can perceive at a frequency of 1000 Hz. Sound intensity level is not the same as intensity. Because β β is defined in terms of a ratio, it is a unitless quantity telling you the level of the sound relative to a fixed standard ( 10 –12 W/m 2 10 –12 W/m 2 , in this case). The units of decibels (dB) are used to indicate this ratio is multiplied by 10 in its definition. The bel, upon which the decibel is based, is named for Alexander Graham Bell, the inventor of the telephone.

The decibel level of a sound having the threshold intensity of 10 – 12 W/m 2 10 – 12 W/m 2 is β = 0 dB β = 0 dB , because log 10 1 = 0 log 10 1 = 0 . That is, the threshold of hearing is 0 decibels. Table 17.2 gives levels in decibels and intensities in watts per meter squared for some familiar sounds.

One of the more striking things about the intensities in Table 17.2 is that the intensity in watts per meter squared is quite small for most sounds. The ear is sensitive to as little as a trillionth of a watt per meter squared—even more impressive when you realize that the area of the eardrum is only about 1 cm 2 1 cm 2 , so that only 10 – 16 10 – 16 W falls on it at the threshold of hearing! Air molecules in a sound wave of this intensity vibrate over a distance of less than one molecular diameter, and the gauge pressures involved are less than 10 – 9 10 – 9 atm.

Another impressive feature of the sounds in Table 17.2 is their numerical range. Sound intensity varies by a factor of 10 12 10 12 from threshold to a sound that causes damage in seconds. You are unaware of this tremendous range in sound intensity because how your ears respond can be described approximately as the logarithm of intensity. Thus, sound intensity levels in decibels fit your experience better than intensities in watts per meter squared. The decibel scale is also easier to relate to because most people are more accustomed to dealing with numbers such as 0, 53, or 120 than numbers such as 1 . 00 × 10 – 11 1 . 00 × 10 – 11 .

One more observation readily verified by examining Table 17.2 or using I = ( Δ p ) 2 ρv w 2 I = ( Δ p ) 2 ρv w 2 is that each factor of 10 in intensity corresponds to 10 dB. For example, a 90 dB sound compared with a 60 dB sound is 30 dB greater, or three factors of 10 (that is, 10 3 10 3 times) as intense. Another example is that if one sound is 10 7 10 7 as intense as another, it is 70 dB higher. See Table 17.3 .

Example 17.2

Calculating sound intensity levels: sound waves.

Calculate the sound intensity level in decibels for a sound wave traveling in air at 0ºC 0ºC and having a pressure amplitude of 0.656 Pa.

We are given Δ p Δ p , so we can calculate I I using the equation I = ( Δ p ) 2 / ( 2 pv w ) 2 I = ( Δ p ) 2 / ( 2 pv w ) 2 . Using I I , we can calculate β β straight from its definition in β dB = 10 log 10 ( I / I 0 ) β dB = 10 log 10 ( I / I 0 ) .

(1) Identify knowns:

Sound travels at 331 m/s in air at 0ºC 0ºC .

Air has a density of 1.29 kg /m 3 1.29 kg /m 3 at atmospheric pressure and 0ºC 0ºC .

(2) Enter these values and the pressure amplitude into I = ( Δ p ) 2 / ( 2 ρv w ) I = ( Δ p ) 2 / ( 2 ρv w ) :

(3) Enter the value for I I and the known value for I 0 I 0 into β dB = 10 log 10 ( I / I 0 ) β dB = 10 log 10 ( I / I 0 ) . Calculate to find the sound intensity level in decibels:

This 87 dB sound has an intensity five times as great as an 80 dB sound. So a factor of five in intensity corresponds to a difference of 7 dB in sound intensity level. This value is true for any intensities differing by a factor of five.

Example 17.3

Change intensity levels of a sound: what happens to the decibel level.

Show that if one sound is twice as intense as another, it has a sound level about 3 dB higher.

You are given that the ratio of two intensities is 2 to 1, and are then asked to find the difference in their sound levels in decibels. You can solve this problem using of the properties of logarithms.

The ratio of the two intensities is 2 to 1, or:

We wish to show that the difference in sound levels is about 3 dB. That is, we want to show:

(2) Use the definition of β β to get:

This means that the two sound intensity levels differ by 3.01 dB, or about 3 dB, as advertised. Note that because only the ratio I 2 / I 1 I 2 / I 1 is given (and not the actual intensities), this result is true for any intensities that differ by a factor of two. For example, a 56.0 dB sound is twice as intense as a 53.0 dB sound, a 97.0 dB sound is half as intense as a 100 dB sound, and so on.

It should be noted at this point that there is another decibel scale in use, called the sound pressure level , based on the ratio of the pressure amplitude to a reference pressure. This scale is used particularly in applications where sound travels in water. It is beyond the scope of most introductory texts to treat this scale because it is not commonly used for sounds in air, but it is important to note that very different decibel levels may be encountered when sound pressure levels are quoted. For example, ocean noise pollution produced by ships may be as great as 200 dB expressed in the sound pressure level, where the more familiar sound intensity level we use here would be something under 140 dB for the same sound.

Take-Home Investigation: Feeling Sound

Find a CD player and a CD that has rock music. Place the player on a light table, insert the CD into the player, and start playing the CD. Place your hand gently on the table next to the speakers. Increase the volume and note the level when the table just begins to vibrate as the rock music plays. Increase the reading on the volume control until it doubles. What has happened to the vibrations?

Check Your Understanding

Describe how amplitude is related to the loudness of a sound.

Amplitude is directly proportional to the experience of loudness. As amplitude increases, loudness increases.

Identify common sounds at the levels of 10 dB, 50 dB, and 100 dB.

10 dB: Running fingers through your hair.

50 dB: Inside a quiet home with no television or radio.

100 dB: Take-off of a jet plane.

• 1 Several government agencies and health-related professional associations recommend that 85 dB not be exceeded for 8-hour daily exposures in the absence of hearing protection.

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Access for free at https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units

• Authors: Paul Peter Urone, Roger Hinrichs
• Publisher/website: OpenStax
• Book title: College Physics 2e
• Publication date: Jul 13, 2022
• Location: Houston, Texas
• Book URL: https://openstax.org/books/college-physics-2e/pages/1-introduction-to-science-and-the-realm-of-physics-physical-quantities-and-units
• Section URL: https://openstax.org/books/college-physics-2e/pages/17-3-sound-intensity-and-sound-level

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Dictation: Instructions 2.1

4. Show Answer 4. Hide Answer

• Elementary dictation exercises
• Intermediate dictation exercises
• Advanced dictation exercises

4.2. Half Steps and Whole Steps *

The pitch of a note is how high or low it sounds. Musicians often find it useful to talk about how much higher or lower one note is than another. This distance between two pitches is called the interval between them. In Western music , the small interval from one note to the next closest note higher or lower is called a half step or semi-tone .

Figure 4.8. Half Steps

Listen to the half steps in Figure 4.8 .

The intervals in Figure 4.8 look different on a staff ; sometimes they are on the same line, sometimes not. But it is clear at the keyboard that in each case there is no note in between them.

So a scale that goes up or down by half steps, a chromatic scale , plays all the notes on both the white and black keys of a piano. It also plays all the notes easily available on most Western instruments. (A few instruments, like trombone and violin, can easily play pitches that aren't in the chromatic scale, but even they usually don't.)

Figure 4.9. One Octave Chromatic Scale

Listen to a chromatic scale.

If you go up or down two half steps from one note to another, then those notes are a whole step , or whole tone apart.

Figure 4.10. Whole Steps

A whole tone scale , a scale made only of whole steps, sounds very different from a chromatic scale.

Figure 4.11. Whole Tone Scale

Listen to a whole tone scale.

You can count any number of whole steps or half steps between notes; just remember to count all sharp or flat notes (the black keys on a keyboard) as well as all the natural notes (the white keys) that are in between.

Example 4.2. 

The interval between C and the F above it is 5 half steps, or two and a half steps.

Figure 4.12. 

Exercise 4.2.1. ( Go to Solution )

Identify the intervals below in terms of half steps and whole steps. If you have trouble keeping track of the notes, use a piano keyboard, a written chromatic scale, or the chromatic fingerings for your instrument to count half steps.

Figure 4.13. 

Exercise 4.2.2. ( Go to Solution )

Fill in the second note of the interval indicated in each measure. 

Figure 4.14. 

Solutions to Exercises

Solution to Exercise 4.2.1. ( Return to Exercise )

Figure 4.15. 

Solution to Exercise 4.2.2. ( Return to Exercise )

Figure 4.16. 

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