# Excursions in Physics

## Homework, Chapter 12: Sound and Music

(this is Chapter 12 of Adventures in Physics, available only online)

Ch 12, Sound and Music; 1, 2, 5, 8, 10, 12, 14, 15, 16, 20, 22

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1. What is a longitudinal wave?

In a longitudinal wave, the individual disturbances that make up the wave are in the same direction as the wave itself. Examples of a longitudinal wave are a Slinky and sound. A longitudinal wave is in contrast to a transverse wave. In a transverse wave, the individual disturbances that make up the wave are perpendicular to the direction of the wave itself. A good example of a transverse wave is a wave on a rope.

2. How will the frequency of the sound used for echolocation affect the size of objects that can be detected? Will higher or lower frequencies allow for detection of smaller objects with echolocation?

The wavelength of a wave determines how it will be reflected. The shorter wavelengths of higher frequencies mean that the echolocation of bats and dolphins help them identify more detail -- or smaller objects -- than would be possible with longer wavelengths or lower frequencies.

3. To the good ear of a careful listener, a difference can be heard when the same violin string is plucked at different locations. Why would this be?

Plucking a string in different places will excite different amounts of different kinds of standing waves. So a careful listener will, indeed, be able to tell a difference.

4. As a scale is played on a piano, from low to high, the pitch or frequency of the sound increases. What happens to the wavelength?

speed = frequency x wavelength

As the frequency increases, the wavelength decreases. That means that higher frequencies correspond to shorter wavelengths.

5. For strings of the same length and tension, why would a heavier, thicker guitar string produce a lower pitch than a lighter, thinner one?

Experimentally, we will find that the velocity of a wave on a string is related to the tension in the string T and the linear mass density (mass per unit length) by
v2 = T /

or

So a larger linear mass density will give a smaller value for v, the speed of the wave on the string. The wavelength of the standing wave is determined by the length of the string. So a smaller value for v, the speed of the wave on the string, means the frequency will be smaller (or lower) since

wave speed = wavelength x frequency

Another way to think of this is just to think that the greater mass will respond more slowly simply due to Newton's Second Law of Motion,

F = m a

so a more massive string will produce a lower frequency.

6. In terms of standing waves, explain why long organ pipes produce sound of lower pitch than short pipes.

Longer pipes have longer wavelengths for standing waves; this means lower fundamental frequencies.

7. In a good audio system, why is the low-frequency speaker (the woofer) much larger than the high-frequency speaker (tweeter)?

Low-frequency sound waves have a l-o-n-g wavelength and l-o-n-g wavelength waves are produced more efficiently with a larger speaker. Larger speakers have more mass so their resonant frequency is lower.

8. If a guitar string is very lightly touched at its mid-point, the pitch heard will shift to an octave higher. Explain why.

Lightly touching a guitar string at its mid-point will stop the vibration of the fundamental frequency (and other harmonics) that has an antinode there. It will not affect the next higher harmonic that has a node at the center. This next higher harmonic has a wavelength of one-half that of the harmonic; that means its pitch is twice as high as the fundamental frequency -- and that is an octave higher.

10. Why is the speed of sound so much greater in liquids and solids than in air?

Molecules that compose a liquid or a solid are held in place far more strongly than the molecules that compose air (or any gas). Any disturbance of a molecule in a liquid or solid means that molecule is pulled back to its equilibrium position (and then coasts on beyond that) far faster than for a molecule in a gas.

11. Why will the temperature in a concert hall affect the pitch of the instruments?

wave speed = frequency x wavelength

Wave speed depends upon temperature so the frequency and wavelength of the standing waves that produce the sound in an instrument also depend upon temperature. A band that is tuned inside a nice warm building will soon be out of tune as they march into a cold open, outdoor stadium.

12. Why do you see lightning before you hear the thunder it produces?

The speed of light is very great (3.0 x 108 m/s). It is far, far greater than the speed of sound (about 345 m/s). If you see distant lightning, the light arrives at your eye immediately but it requires about four minutes for the sound to travel a mile.

14. What is the same when you hear a high C played on a French horn and a high C played on a piano?

The fundamental frequency -- the lowest frequency heard -- is the same for both instruments.

15. Why does a high C played on a French horn sound different from a high C played on a piano?

The two instruments have a different set of harmonics -- also called overtones -- which gives each instrument its distinctive "voice" or quality or timbre.

16. How many octaves are there on a standard piano keyboard?

A standard piano keyboard has 88 keys and there are 12 keys to an octave.
N = 88 / 12 = 7.3 octaves

20. Suppose you stand at an intersection and listen to an ambulance as it approaches you and then goes away from you. Explain what you will hear.

As the ambulance approaches, you hear its siren with a pitch that is higher than if it were standing still. As it goes away from you, you hear its siren with a pitch that is lower than if it were standing still. This is an example of the Doppler Effect.

22. Supersonic flights that are restricted over land are allowed over the ocean. Does this mean there is no pressure wave--or sonic boom--created over the ocean?

There is still a sonic boom over the ocean. But there are far fewer people to be disturbed than on land.

Typical Multiple Choice Questions:

1. Light and sound are both waves. You can see a ringing bell inside an evacuated glass container but you can not hear it. This is because

A) of resonance

B) light travels faster than sound

C) sound requires air to be transmitted and light does not

D) light passes through glass but sound does not

2. Sound is

A) an electromagnetic wave

B) a polarized wave

C) a transverse wave

D) a longitudinal wave

3. "Supersonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

4. "Ultrasonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

5. "Infrasonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

6. Bats and dolphins use echolocation to navigate or the find food or to find their way without relying on sight. The frequencies they use are

A) supersonic

B) infrasonic

C) ultrasonic

D) microsonic

7. If you double the frequency of a sound wave, you also double its

A) wavelength

B) speed

C) amplitude

D) all of the above

8. The range of human hearing is about

A) 10 Hz to 100 Hz

B) 50 Hz to 500 Hz

C) 50 Hz to 20 000 Hz

D) 1 000 Hz to 100 000 Hz

9. Sound travels fastest in

A) air (a gas)

B) water (a liquid)

C) steel (a solid)

D) vacuum

10. The speed of sound in air depends upon

A) wavelength

B) frequency

C) temperature

D) amplitude

11. Increasing the length of a vibrating string will

A) decrease its resonance frequency

B) decrease its amplitude

C) increase its amplitude

D) increase its resonance frequency

12. Ella Fitzgerald made commercials for Memorex in which she used her voice to break a wine glass. This is an example of

A) echolocation

B) reflected sound

C) ultrasonic frequencies

D) resonance

13. Beats are heard when two sounds have

A) nearly the same amplitude

B) nearly the same frequencies

C) twice the amplitude

D) exactly twice the wavelength

14. The fundamental frequency present in a sound is the

A) sum of all the frequencies mixed together

B) difference between the highest and lowest frequencies present

C) lowest frequency present

D) highest frequency present

15. The "pitch" of a sound is determined by its

A) overtones frequencies

B) harmonics frequencies

C) fundamental frequency

D) resonance frequencies

16. The quality or timbre -- the distincitive characteristic -- of a sound is determined by its

A) overtones or harmonics

B) amplitude or loudness

C) attack or decay

D) fundamental frequency

17. You hear beats with a frequency of 3 Hz when you strike a tuning fork that vibrates at 256 Hz and a chime. The chime has a frequency of

A) 3 x 256 Hz = 768 Hz

B) 259 Hz

C) (256 / 3) Hz = 85.3 Hz

D) 250 Hz

18. The fundamental frequency of a violin string is 440 hertz. The frequency of its second harmonic is

A) 110 Hz

B) 220 Hz

C) 440 Hz

D) 880 Hz

19. Consider a musical note of 440 hertz ("concert 'A'"). Two octaves higher is represented by a musical note of

A) 220 Hz

B) 880 Hz

C) 1320 Hz

D) 1760 Hz

20. The intensity or loudness of a musical sound is related to the sound wave's

A) wavelength

B) frequency

C) amplitude

D) wave speed

21. Suppose you play a note of a certain pitch on a violin. You can produce a lower-pitched note by

A) shortening the length of the string that is allowed to vibrate

B) increasing the tension of the string

C) decreasing the linear mass density of the string

D) lengthening the part of the string that vibrates.

Answers to these Typical Multiple Choice Questions:

1. Light and sound are both waves. You can see a ringing bell inside an evacuated glass container but you can not hear it. This is because

A) of resonance

B) light travels faster than sound

C) sound requires air to be transmitted and light does not

D) light passes through glass but sound does not

2. Sound is

A) an electromagnetic wave
light is an electromagnetic wave

radio and television and X-rays are also electromagnetic waves

B) a polarized wave

only transverse waves can be polarized

longitudinal waves can not be polarized

C) a transverse wave

D) a longitudinal wave

3. "Supersonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

4. "Ultrasonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

Rangefinders on Polaroid cameras use ultrasound.

Ultrasound is used for medical imaging.

Bats and dolphins use ultrasound for echolocation.

C) faster than the speed of sound

D) slower than the speed of sound

5. "Infrasonic" means

A) lower than the range of human hearing

B) higher than the range of human hearing

C) faster than the speed of sound

D) slower than the speed of sound

6. Bats and dolphins use echolocation to navigate or the find food or to find their way without relying on sight. The frequencies they use are

A) supersonic

B) infrasonic

C) ultrasonic

Both bats and dolphins use ultrasound with frequencies of about 50 kHz and above.

D) microsonic

7. If you double the frequency of a sound wave, you also double its

A) wavelength; doubling the frequency means you reduce the wavelength to one-half

B) speed; changing the frequency should have no effect on the speed.

C) amplitude ; changing the frequency should have no effect on the amplitude.

D) all of the above

E) none of the above

8. The range of human hearing is about

A) 10 Hz to 100 Hz

B) 50 Hz to 500 Hz

C) 50 Hz to 20 000 Hz

D) 1 000 Hz to 100 000 Hz

9. Sound travels fastest in

A) air (a gas)

B) water (a liquid)

C) steel (a solid)

The inter-molecular forces that hold a molecule in place in a solid are much stronger than those in a liquid or a gas so they move the molecule more rapidly -- just like a mass attached to a stronger spring. This more rapid movement of the molecules means that sound is transmitted faster too.

D) vacuum

10. The speed of sound in air depends upon

A) wavelength

B) frequency

C) temperature

D) amplitude

11. Increasing the length of a vibrating string will

A) decrease its resonance frequency
Increasing the length of the string means the wavelength of the standing wave is also increased. And increase in wavelength means a decrease in the frequency.

B) decrease its amplitude

C) increase its amplitude

D) increase its resonance frequency

12. Ella Fitzgerald made commercials for Memorex in which she used her voice to break a wine glass. This is an example of

A) echolocation

B) reflected sound

C) ultrasonic frequencies

D) resonance

13. Beats are heard when two sounds have

A) nearly the same amplitude

B) nearly the same frequencies

C) twice the amplitude

D) exactly twice the wavelength

14. The fundamental frequency present in a sound is the

A) sum of all the frequencies mixed together

B) difference between the highest and lowest frequencies present

C) lowest frequency present

D) highest frequency present

15. The "pitch" of a sound is determined by its

A) overtones frequencies

B) harmonics frequencies

C) fundamental frequency

D) resonance frequencies

16. The quality or timbre -- the distincitive characteristic -- of a sound is determined by its

A) overtones or harmonics

B) amplitude or loudness

C) attack or decay

D) fundamental frequency

17. You hear beats with a frequency of 3 Hz when you strike a tuning fork that vibrates at 256 Hz and a chime. The chime has a frequency of

A) 3 x 256 Hz = 768 Hz

B) 259 Hz

fbeat = difference in frequencies = f2 - f1 = 3 Hz

3 Hz = f2 - 256 Hz

f2 = 259 Hz

C) (256 / 3) Hz = 85.3 Hz

D) 250 Hz

18. The fundamental frequency of a violin string is 440 hertz. The frequency of its second harmonic is

A) 110 Hz

B) 220 Hz

C) 440 Hz

D) 880 Hz

19. Consider a musical note of 440 hertz ("concert 'A'"). Two octaves higher is represented by a musical note of

A) 220 Hz; this is one octave lower.

B) 880 Hz ; this is one octave higher.

C) 1320 Hz

D) 1760 Hz

One octave above A at 440 Hz is twice that frequency, 880 Hz.

One octave above that A at 880 Hz is 1760 Hz.

20. The intensity or loudness of a musical sound is related to the sound wave's

A) wavelength

B) frequency

C) amplitude

D) wave speed

21. Suppose you play a note of a certain pitch on a violin. You can produce a lower-pitched note by

A) shortening the length of the string that is allowed to vibrate

B) increasing the tension of the string

C) decreasing the linear mass density of the string

D) lengthening the part of the string that vibrates.

The other three choices will each RAISE the pitch of the note.

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