Exercises: Sound

In a laboratory, an electric bell is suspended inside a glass bell jar, and the air is gradually removed. The figure shows the experimental setup.

1. a) Describe what is heard as the air leaves.
2. b) What does this experiment demonstrate about what sound needs in order to travel?
3. c) Why do two astronauts on the surface of the Moon talk to each other by radio even when standing next to each other?

Sound travels through air as a series of compressed and rarefied regions that move from the source to the ear. The figure shows these regions of compression and rarefaction.

1. a) Does the air travel from the loudspeaker to your ear, or does it only oscillate around its position?
2. b) Considering the direction in which the air oscillates relative to the direction in which the wave travels, is sound a transverse or longitudinal wave? Justify your answer.
3. c) Describe how you would model it using a stretched spring on a table.

The loudspeaker at the sports center is $68\ \text{m}$ away from where you are, as shown in the figure.

How long does it take for the sound to reach your ears? Given data: sound travels through air at $340\ \text{m/s}$.

On a guitar, the first string (the thinnest) vibrates open at $330\ \text{Hz}$ and the sixth (the thickest) at $82.5\ \text{Hz}$.

1. a) Which of the two strings sounds higher-pitched?
2. b) Which wave quantity determines the pitch (high or low) of a sound?
3. c) In what unit is this quantity measured?

Two people play the same key on a piano, one much harder than the other.

1. a) Which of the two sounds is heard louder?
2. b) The loudness of a sound (loud or quiet) is related to the property called intensity: which wave quantity does it depend on?
3. c) Does the pitch of the note change when it is played harder? Justify your answer.

A healthy young human ear perceives sounds between roughly $20\ \text{Hz}$ and $20\,000\ \text{Hz}$. State whether we can hear each of these sounds and name the range to which they belong:

1. a) A sound of $15\ \text{Hz}$.
2. b) A sound of $440\ \text{Hz}$.
3. c) A sound of $25\,000\ \text{Hz}$.

What are sounds with frequencies above $20\,000\ \text{Hz}$ called, and which animal uses them to navigate in the dark?

A violin and a flute play the same note, an A at $440\ \text{Hz}$, at the same volume. The figure shows the waveform produced by each instrument.

1. a) Why can we still distinguish which instrument is playing?
2. b) What is this sound quality called? Explain how the waves produced by each instrument differ.

During a thunderstorm, you see lightning and count $4\ \text{s}$ until you hear the thunder, as shown in the figure.

1. a) How far away from you is the thunderstorm? (Sound travels at $340\ \text{m/s}$.)
2. b) Why can you neglect the time it takes for the light from the lightning to reach you?

You shout in front of a court wall and hear the echo $0.5\ \text{s}$ later, as shown in the figure.

1. a) Explain the path travelled by the sound from when it left your mouth until you heard it.
2. b) Calculate how far away the wall is. (Sound travels at $340\ \text{m/s}$.)

Fireworks explode $1700\ \text{m}$ from your house. How long does it take for you to hear the bang after seeing the flash? (Sound travels at $340\ \text{m/s}$.)

A whistle emits a sound of $340\ \text{Hz}$ in air, where sound travels at $340\ \text{m/s}$.

1. a) Calculate its wavelength.
2. b) Another whistle emits at double the frequency, $680\ \text{Hz}$: calculate its wavelength.
3. c) Explain, using $v = \lambda \times f$, how the wavelength of a sound changes when its frequency increases in the same medium.

A loudspeaker generates a pure tone of $200\ \text{Hz}$ in air.

1. a) Calculate the period of the wave.
2. b) Calculate its wavelength. (Sound travels at $340\ \text{m/s}$.)

Sound travels through seawater at around $1500\ \text{m/s}$. Two dolphins are swimming $3\ \text{km}$ apart.

1. a) How long does it take for the sound from one dolphin to reach the other through the water?
2. b) How long would it take to cover the same distance through the air? (In air, sound travels at $340\ \text{m/s}$; give the answer to one decimal place.)
3. c) In which of the two media does sound travel faster?

A mountain guide shouts towards a gorge wall located $170\ \text{m}$ away.

1. a) What total distance does the sound travel from the moment he shouts until he hears the echo?
2. b) How long will it take for him to hear the echo? (Sound travels at $340\ \text{m/s}$.)

A whale sings at $20\ \text{Hz}$ and a bat emits calls at $68\,000\ \text{Hz}$.

1. a) Can the human ear perceive both sounds? Justify your answer using the hearing range, from $20\ \text{Hz}$ to $20\,000\ \text{Hz}$.
2. b) Calculate the wavelength of each sound in air and give it in a suitable unit. (Sound travels at $340\ \text{m/s}$.)
3. c) Relate the very small wavelength of the bat's calls to its ability to detect tiny insects.

In a city, traffic, roadworks, outdoor bar terraces playing music and ambulance sirens coexist.

1. a) Explain what is meant by noise pollution.
2. b) State two effects of excessive noise on human health.
3. c) Propose one measure to reduce noise by acting at the source, and another by acting on the medium through which it travels.

A hiker shouts in front of a distant rock face and hears the echo $3\ \text{s}$ later.

1. a) How far away is the wall? (Sound travels at $340\ \text{m/s}$.)
2. b) They walk $170\ \text{m}$ towards the rock face and shout again: how long does the echo take now?
3. c) Explain why the time has decreased in the same proportion as the distance.

A ship's sonar sends an ultrasound pulse towards the seabed and the echo returns $0.4\ \text{s}$ later, as shown in the figure. Sound travels through water at $1500\ \text{m/s}$.

1. a) What is the depth under the ship?
2. b) Why does sonar use ultrasound instead of audible sound?
3. c) If the ship sails to an area where the seabed is at $600\ \text{m}$, how long will it take for the echo to return?

There is a rule of thumb for thunderstorms: "every $3\ \text{s}$ between the lightning and the thunder means $1\ \text{km}$ of distance".

1. a) Check the rule by calculating what distance sound travels in $3\ \text{s}$ ($v_{\text{sound}} = 340\ \text{m/s}$).
2. b) What error does the rule make, in meters and as a percentage? Do you find this acceptable for everyday use?
3. c) The rule assumes that light arrives instantaneously: calculate how long light from the lightning actually takes to travel $1\ \text{km}$ ($c = 3\times10^{8}\ \text{m/s}$) and justify whether this assumption is reasonable.

In Western films, scouts put their ear to the railway track to find out if a train is approaching. Sound travels through steel at $5000\ \text{m/s}$ and through air at $340\ \text{m/s}$. A distant train blows its whistle from a distance of $1700\ \text{m}$. The figure shows the two paths by which the sound arrives.

1. a) How long does it take for the whistle sound to arrive through the air?
2. b) How long does it take to arrive along the track?
3. c) How much earlier does the sound arrive along the track? Give your answer to one decimal place.
4. d) Thinking about the particles in each medium, explain why sound travels much faster through steel than through air.

Two students want to measure the speed of sound outdoors. They stand $255\ \text{m}$ apart: one hits a bass drum and the other times $0.75\ \text{s}$ from seeing the strike to hearing the sound.

1. a) Calculate the speed of sound that they obtain.
2. b) Why does the second student start the stopwatch upon seeing the strike and not need to know the exact moment it occurred?
3. c) State two sources of error in this measurement and one way to improve the experiment.

At an outdoor concert, the sound next to the loudspeakers is deafening, whereas $100\ \text{m}$ away it is barely bothersome. The figure represents how the wave energy spreads out as it moves away from the loudspeaker.

1. a) Which property of the sound wave decreases with distance from the source, and which remains constant?
2. b) The loudspeaker emits its energy, spreading it over increasingly large spherical surfaces as the wave travels away: using this idea, explain why the volume drops so much with distance.
3. c) Relate the above to the recommendation not to stand right next to loudspeakers for long periods.

A family lives in an apartment next to a busy avenue and suffers from traffic noise at night as well.

1. a) Propose a measure to reduce noise by acting on the source, another by acting on the medium of propagation, and another on the receiver, justifying each physically.
2. b) Explain why a double-glazed window with a cavity insulating layer reduces noise better than single glazing.
3. c) Indoors, thick curtains, carpets and bookshelves filled with books reduce noise: what do these materials do to the sound instead of reflecting it?

A bat emits an ultrasound pulse and receives the echo produced by a moth $0.02\ \text{s}$ later. (Sound travels through air at $340\ \text{m/s}$.)

1. a) How far away is the moth?
2. b) Why can humans not hear the bat's calls?
3. c) Objects much smaller than the wavelength barely reflect the wave: explain why it is advantageous for the bat to use high frequencies with short wavelengths to hunt insects.