Objectives Chapter 13

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Section 1 Sound Waves

Chapter 13

Objectives

• Explain how sound waves are produced.

• Relate frequency to pitch.

• Compare the speed of sound in various media.

• Relate plane waves to spherical waves.

• Recognize the Doppler effect, and determine the direction of a frequency shift when there is relative motion between a source and an observer.

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Using a Tuning Fork to Produce a Sound Wave

• A tuning fork will produce a pure musical note

• As the tines vibrate, they disturb the air near them

• As the tine swings to the right, it forces the air

molecules near it closer together

• This produces a high density area in the air

– This is an area of compression

Section 14.1

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Using a Tuning Fork, cont.

• As the tine moves toward the left, the air molecules to the right of the tine

spread out

• This produces an area of low density

– This area is called a rarefaction

Section 14.1

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Using a Tuning Fork, final

• As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork

• A sinusoidal curve can be used to represent the longitudinal wave

– Crests correspond to compressions and troughs to rarefactions

Section 14.1

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Frequency of Sound Waves

• As discussed earlier, frequency is defined as the number of cycles per unit of time.

• Sound waves that the average human ear can hear, called audible sound waves, have frequencies

between 20 and 20 000 Hz.

• Sound waves with frequencies less than 20 Hz are called infrasonic waves.

• Sound waves with frequencies above 20 000 Hz are called ultrasonic waves.

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Frequency and Pitch

• The frequency of an audible sound wave determines how high or low we perceive the sound to be, which is known as pitch.

• As the frequency of a sound wave increases, the pitch rises.

• The frequency of a wave is an objective quantity that can be measured, while pitch refers to how different frequencies are perceived by the human ear.

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The Speed of Sound

• The speed of sound depends on the medium.

– Because waves consist of particle vibrations, the speed of a wave depends on how quickly one

particle can transfer its motion to another particle.

– For example, sound waves generally travel faster through solids than through gases because the

molecules of a solid are closer together than those of a gas are.

• The speed of sound also depends on the

temperature of the medium. This is most noticeable with gases.

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The Speed of Sound in Various Media

On a typical summer day (25°𝐶), how far

does sound travel in 1 second?

What is the wavelength of a 500 Hz sound

wave?

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You are 100 m from a

dolphin. The dolphin emits a 20 000 Hz noise (ouch!), how long will it take until you hear it underwater?

What if the two of you were above water?

What is the wavelength of the noise in water?

What is the wavelength above water?

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You see lightning off in the distance, and start to

count. It takes 5.2 seconds until you hear the thunder.

How far away is the lightning?

1 minute later, you see

lightning again, but it only takes 4.2 s to hear the

thunder. How fast is the thunderstorm moving?

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The Propagation of Sound Waves

• The radial lines perpendicular to the wave fronts are called rays.

• The sine curve used in our previous representation corresponds to a single ray.

• Sound waves propagate in three dimensions.

• Spherical waves can be represented graphically in two dimensions, as

shown in the diagram.

• The circles represent the centers of compressions, called wave fronts.

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What’s happening here?

• https://www.youtube.com/watch?v=a3RfULw7aAY

• Explained:

https://www.youtube.com/watch?v=I1ykNQijOC8

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Doppler Effect, Case 1

(Observer Toward Source)

• An observer is moving toward a stationary source

• Due to his

movement, the

observer detects an additional number of wave fronts

• The frequency heard is increased

Section 14.6

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Doppler Effect, Case 1

(Observer Away from Source)

• An observer is

moving away from a stationary source

• The observer

detects fewer wave fronts per second

• The frequency appears lower

Section 14.6

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Doppler Effect, Case 2 (Source in Motion)

• As the source moves toward the observer (A), the wavelength

appears shorter and the frequency increases

• As the source moves away from the observer (B), the wavelength

appears longer and the frequency appears to be lower

Section 14.6

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Doppler Effect, Case 2 (Source in Motion)

• As the source moves toward the observer (A), the wavelength

appears shorter and the frequency increases

• As the source moves away from the observer (B), the wavelength

appears longer and the frequency appears to be lower

Section 14.6

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The Doppler Effect

• The Doppler effect is an observed change in

frequency when there is relative motion between the source of waves and an observer.

• Because frequency determines pitch, the Doppler effect affects the pitch heard by each listener.

• Although the Doppler effect is most commonly

experienced with sound waves, it is a phenomenon common to all waves, including electromagnetic

waves, such as visible light.

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Doppler Effect

• Sheldon:

https://www.youtube.com/watch?v=z0EaoilzgGE

• Example:

https://www.youtube.com/watch?v=a3RfULw7aAY

• Explained:

https://www.youtube.com/watch?v=h4OnBYrbCjY

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Practice

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Bellringer

You see lightning off in the

distance, and start to count. It takes 5.2 seconds until you

hear the thunder.

(hint: speed of sound in this air is 346 m/s)

1 minute later, you see

lightning again, but it only

takes 4.2 s to hear the thunder.

How fast is the thunderstorm moving?

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Bellringer

1. You see lightning off in the distance, and start to count. It takes 6.2 seconds until you

hear the thunder.

(hint: speed of sound in this air is 346 m/s)

2. When a car moves toward you honking its horn, is the

frequency shifted higher, lower, or stays the same as normal?

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Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. The sound (v = 345 m/s) bounces off the nearest canyon wall (which is located 170 meters away from Miles) and returns to Miles. Determine the time elapsed between when Miles makes the holler and the echo is heard.

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Lab – Sound Waves and the Speed of Sound

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Preview

• Objectives

• Standing Waves on a Vibrating String

• Standing Waves in an Air Column

• Sample Problem

• Timbre

• Beats

Chapter 13 Section 3 Harmonics

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Objectives

• Differentiate between the harmonic series of open and closed pipes.

• Calculate the harmonics of a vibrating string and of open and closed pipes.

• Relate harmonics and timbre.

• Relate the frequency difference between two waves to the number of beats heard per second.

Section 3 Harmonics

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Standing Waves on a Vibrating String

• The vibrations on the string of a musical instrument usually consist of many standing waves, each of which has a different wavelength and frequency.

• The greatest possible wavelength on a string of length L is ^{= 2L}^.

• The fundamental frequency, which corresponds to this wavelength, is the lowest frequency of vibration.

1

1 2

 v  v

f L

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Standing Waves on a Vibrating String, continued

• Each harmonic is an integral multiple of the fundamental frequency.

• The harmonic series is a series of frequencies that includes the fundamental frequency and integral

multiples of the fundamental frequency.

Harmonic Series of Standing Waves on a Vibrating String Section 3 Harmonics

1, 2,3,...

 2 

n

f n v n

L

(speed of waves on the string) frequency = harmonic number

(2)(length of the vibrating string)



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The Harmonic Series Section 3 Harmonics

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Standing Waves in an Air Column

• If both ends of a pipe are open, the air is free to move easily at ends, so there is an antinode at each end.

• In this case, all harmonics are present, and the

earlier equation for the harmonic series of a vibrating string can be used.

Harmonic Series of a Pipe Open at Both Ends Section 3 Harmonics

1, 2,3,...

 2 

n

f n v n

L

(speed of sound in the pipe) frequency = harmonic number

(2)(length of vibrating air column)



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Resonance in Air Column Open at Both Ends

Antinode at both ends

Section 14.10

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Resonance in an Air Column Closed at One End

The closed end must be a node

The open end is an antinode

There are no even multiples of the

fundamental harmonic

Section 14.10

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Standing Waves in an Air Column, continued

• If one end of a pipe is closed, air cannot move at all there, so there is a node at that end.

• With an antinode at one end and a node at the other end, a different set of standing waves occurs.

• In this case, only odd harmonics are present.

Harmonic Series of a Pipe Closed at One End Section 3 Harmonics

1,3,5,...

 4 

n

f n v n

L

(speed of sound in the pipe) frequency = harmonic number

(4)(length of vibrating air column)



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Sample Problem

Harmonics

What are the first three harmonics in a 2.45 m long pipe that is open at both ends? What are the first three

harmonics when one end of the pipe is closed? Assume that the speed of sound in air is 345 m/s.

1. Define Given:

L = 2.45 m v = 345 m/s Unknown:

Case 1: f₁, f₂, f₃ Case 2: f₁, f₃, f₅

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Sample Problem

2. Plan

Choose an equation or situation:

Case 1:

In both cases, the second two harmonics can be found by multiplying the harmonic numbers by the

fundamental frequency.

1, 2,3,...

 2 

n

f n v n

L

1,3,5,...

 4 

n

f n v n

L

Case 2:

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Sample Problem

3. Calculate

Substitute the values into the equation and solve:

Case 1:

1

(345 m/s)

(1) 70.4 Hz

2 (2)(2.45 m)

 

    

 

f n v

L

The next two harmonics are the second and third:

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Sample Problem

Tip: Use the correct harmonic numbers for each situation. For a pipe open at both ends, n = 1, 2, 3, etc. For a pipe closed at one end, only odd harmonics are present, so n = 1, 3, 5, etc.

The next two harmonics are the third and the fifth:

3. Calculate, continued Case 2:

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Bellringer

Harmonics

What are the first three harmonics in a 1.45 m long pipe that is open at both ends? What are the first three

harmonics when one end of the pipe is closed? Assume that the speed of sound in air is 345 m/s.

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Timbre

• Timbre is the the musical quality of a tone resulting from the combination of harmonics present at different intensities.

• A clarinet sounds different from a viola because of differences in timbre, even when both

instruments are sounding the same note at the same volume.

• The rich harmonics of most instruments provide a much fuller sound than that of a tuning fork.

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Harmonics of Musical Instruments

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Bellringer 1. A pipe that is open at both ends has a 5^th harmonic with frequency 500 Hz.

What is the fundamental frequency of the pipe?

2. A pipe that is closed at one end has a 3^rd harmonic with a frequency 390 Hz. What is frequency of the next

harmonic that resonates?

https://www.youtube.com/wa tch?v=LOPBospfiU0

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Beats

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Beats

• When two waves of slightly different

frequencies interfere, the interference pattern varies in such a way that a listener hears an alternation between loudness and softness.

• The variation from soft to loud and back to soft is called a beat^.

• In other words, a beat is the periodic variation in the amplitude of a wave that is the superposition of two waves of slightly different frequencies.

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Calculating Beat Frequency

• The beats heard, is the difference between two frequencies.

• Example: if two tuning forks are playing, with frequencies 450 Hz and 458 Hz,

what beat frequency will you hear?

• 458 Hz – 450 Hz =

8 Hz

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Example 2:

• Two vibrating tuning forks held side by side will create a beat frequency of what value if the individual

frequencies of the two forks are

567 Hz and 565 Hz, respectively?

• 567 Hz – 565 Hz = 2 Hz

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Lab

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Mini Lab – Resonance harmonics in tubes

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Homework

• Bring in an instrument so we can analyze the sound waves (if you have one)