# 0.6 Sound  (Page 4/4)

 Page 4 / 4

## Intensity of sound (not included in caps - advanced)

This section is more advanced than required and is best revisited for interest only when you are comfortable with concepts like power and logarithms.

Intensity is one indicator of amplitude. Intensity is the energy transmitted over a unit of area each second.

## Intensity

Intensity is defined as:

$\mathrm{Intensity}=\frac{\mathrm{energy}}{\mathrm{time}×\mathrm{area}}=\frac{\mathrm{power}}{\mathrm{area}}$

By the definition of intensity, we can see that the units of intensity are

$\frac{\mathrm{Joules}}{\mathrm{s}·{\mathrm{m}}^{2}}=\frac{\mathrm{Watts}}{{\mathrm{m}}^{2}}$

The unit of intensity is the decibel (symbol: dB). This reduces to an SI equivalent of $\mathrm{W}·{\mathrm{m}}^{-2}$ .

The average threshold of hearing is ${10}^{-12}\phantom{\rule{3.33333pt}{0ex}}\mathrm{W}·{\mathrm{m}}^{-2}$ . Below this intensity, the sound is too soft for the ear to hear. The threshold of pain is $1.0\phantom{\rule{3.33333pt}{0ex}}\mathrm{W}·{\mathrm{m}}^{-2}$ . Above this intensity a sound is so loud it becomes uncomfortable for the ear.

Notice that there is a factor of ${10}^{12}$ between the thresholds of hearing and pain. This is one reason we define the decibel (dB) scale.

## Db scale

The intensity in dB of a sound of intensity $I$ , is given by:

$\beta =10\phantom{\rule{3.33333pt}{0ex}}log\frac{I}{{I}_{o}}\phantom{\rule{2.em}{0ex}}\phantom{\rule{2.em}{0ex}}{I}_{o}={10}^{-12}\phantom{\rule{3.33333pt}{0ex}}\mathrm{W}·{\mathrm{m}}^{-2}$

In this way we can compress the whole hearing intensity scale into a range from 0 dB to 120 dB.

 Source Intensity (dB) Times greater than hearing threshold Rocket Launch 180 ${10}^{18}$ Jet Plane 140 ${10}^{14}$ Threshold of Pain 120 ${10}^{12}$ Rock Band 110 ${10}^{11}$ Subway Train 90 ${10}^{9}$ Factory 80 ${10}^{8}$ City Traffic 70 ${10}^{7}$ Normal Conversation 60 ${10}^{6}$ Library 40 ${10}^{4}$ Whisper 20 ${10}^{2}$ Threshold of hearing 0 0

Notice that there are sounds which exceed the threshold of pain. Exposure to these sounds can cause immediate damage to hearing.In fact, exposure to sounds from 80 dB and above can damage hearing over time. Measurescan be taken to avoid damage, such as wearing earplugs or ear muffs. Limiting exposure time andincreasing distance between you and the source are also important steps for protecting your hearing.

## Discussion : importance of safety equipment

Working in groups of 5, discuss the importance of safety equipment such as ear protectors for workers in loud environments, e.g. those who use jack hammers or direct aeroplanes to their parking bays. Write up your conclusions in a one page report. Some prior research into the importance of safety equipment might be necessary to complete this group discussion.

## Summary

1. Sound waves are longitudinal waves
2. The frequency of a sound is an indication of how high or low the pitch of the sound is.
3. The human ear can hear frequencies from 20 to 20 000 Hz. Infrasound waves have frequencies lower than 20 Hz. Ultrasound waves have frequencies higher than 20 000 Hz.
4. The amplitude of a sound determines its loudness or volume.
5. The tone is a measure of the quality of a sound wave.
6. The speed of sound in air is around $340\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . It is dependent on the temperature, height above sea level and the phase of the medium through which it is travelling.
7. Sound travels faster when the medium is hot.
8. Sound travels faster in a solid than a liquid and faster in a liquid than in a gas.
9. Sound travels faster at sea level where the air pressure is higher.
10. The intensity of a sound is the energy transmitted over a certain area. Intensity is a measure of frequency.
11. Ultrasound can be used to form pictures of things we cannot see, like unborn babies or tumors.
12. Echolocation is used by animals such as dolphins and bats to “see” their surroundings by using ultrasound.
13. Ships use sonar to determine how deep the ocean is or to locate shoals of fish.

## Exercises

1. Choose a word from column B that best describes the concept in column A.
 Column A Column B pitch of sound amplitude loudness of sound frequency quality of sound speed waveform
2. A tuning fork, a violin string and a loudspeaker are producing sounds. This is because they are all in a state of:
1. compression
2. rarefaction
3. rotation
4. tension
5. vibration
3. What would a drummer do to make the sound of a drum give a note of lower pitch?
1. hit the drum harder
2. hit the drum less hard
3. hit the drum near the edge
4. loosen the drum skin
5. tighten the drum skin
4. What is the approximate range of audible frequencies for a healthy human?
1. 0.2 Hz $\to$ 200 Hz
2. 2 Hz $\to$ 2 000 Hz
3. 20 Hz $\to$ 20 000 Hz
4. 200 Hz $\to$ 200 000 Hz
5. 2 000 Hz $\to$ 2 000 000 Hz
5. X and Y are different wave motions. In air, X travels much faster than Y but has a much shorter wavelength. Which types of wave motion could X and Y be?
 X Y A microwaves red light B radio infra red C red light sound D sound ultraviolet E ultraviolet radio
6. Astronauts are in a spaceship orbiting the moon. They see an explosion on the surface of the moon. Why can they not hear the explosion?
1. explosions do not occur in space
2. sound cannot travel through a vacuum
3. sound is reflected away from the spaceship
4. sound travels too quickly in space to affect the ear drum
5. the spaceship would be moving at a supersonic speed
7. A man stands between two cliffs as shown in the diagram and claps his hands once. Assuming that the velocity of sound is $330\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ , what will be the time interval between the two loudest echoes?
1. $\frac{2}{3}\phantom{\rule{2pt}{0ex}}\mathrm{s}$
2. $\frac{1}{6}\phantom{\rule{2pt}{0ex}}\mathrm{s}$
3. $\frac{5}{6}\phantom{\rule{2pt}{0ex}}\mathrm{s}$
4. 1 s
5. $\frac{1}{3}\phantom{\rule{2pt}{0ex}}\mathrm{s}$
8. A dolphin emits an ultrasonic wave with frequency of 0,15 MHz. The speed of the ultrasonic wave in water is $1 500\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ . What is the wavelength of this wave in water?
1. 0,1 mm
2. 1 cm
3. 10 cm
4. 10 m
5. 100 m
9. The amplitude and frequency of a sound wave are both increased. How are the loudness and pitch of the sound affected?
 loudness pitch A increased raised B increased unchanged C increased lowered D decreased raised E decreased lowered
10. A jet fighter travels slower than the speed of sound. Its speed is said to be:
1. Mach 1
2. supersonic
3. subsonic
4. hypersonic
5. infrasonic
11. A sound wave is different from a light wave in that a sound wave is:
1. produced by a vibrating object and a light wave is not.
2. not capable of traveling through a vacuum.
3. not capable of diffracting and a light wave is.
4. capable of existing with a variety of frequencies and a light wave has a single frequency.
12. At the same temperature, sound waves have the fastest speed in:
1. rock
2. milk
3. oxygen
4. sand
13. Two sound waves are traveling through a container of nitrogen gas. The first wave has a wavelength of 1,5 m, while the second wave has a wavelength of 4,5 m. The velocity of the second wave must be:
1. $\frac{1}{9}$ the velocity of the first wave.
2. $\frac{1}{3}$ the velocity of the first wave.
3. the same as the velocity of the first wave.
4. three times larger than the velocity of the first wave.
5. nine times larger than the velocity of the first wave.
14. Sound travels at a speed of 340 m $·$ s ${}^{-1}$ . A straw is 0,25 m long. The standing wave set up in such a straw with one end closed has a wavelength of 1,0 m. The standing wave set up in such a straw with both ends open has a wavelength of 0,50 m.
1. calculate the frequency of the sound created when you blow across the straw with the bottom end closed.
2. calculate the frequency of the sound created when you blow across the straw with the bottom end open.
15. A lightning storm creates both lightning and thunder. You see the lightning almost immediately since light travels at $3×{10}^{8}\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}$ . After seeing the lightning, you count 5 s and then you hear the thunder. Calculate the distance to the location of the storm.
16. A person is yelling from a second story window to another person standing at the garden gate, 50 m away. If the speed of sound is 344 m $·$ s ${}^{-1}$ , how long does it take the sound to reach the person standing at the gate?
17. A piece of equipment has a warning label on it that says, "Caution! This instrument produces 140 decibels." What safety precaution should you take before you turn on the instrument?
18. What property of sound is a measure of the amount of energy carried by a sound wave?
19. Person 1 speaks to person 2. Explain how the sound is created by person 1 and how it is possible for person 2 to hear the conversation.
20. Sound cannot travel in space. Discuss what other modes of communication astronauts can use when they are outside the space shuttle?
21. An automatic focus camera uses an ultrasonic sound wave to focus on objects. The camera sends out sound waves which are reflected off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 344 m $·$ s ${}^{-1}$ ) returns to the camera 0,150 s after leaving the camera, how far away is the object?
22. Calculate the frequency (in Hz) and wavelength of the annoying sound made by a mosquito when it beats its wings at the average rate of 600 wing beats per second. Assume the speed of the sound waves is 344 m $·$ s ${}^{-1}$ .
23. How does halving the frequency of a wave source affect the speed of the waves?
24. Humans can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 344 m $·$ s ${}^{-1}$ , calculate the wavelength of the sound corresponding to the upper range of audible hearing.
25. An elephant trumpets at 10 Hz. Assuming the speed of sound in air is 344 m $·$ s ${}^{-1}$ , calculate the wavelength of this infrasonic sound wave made by the elephant.
26. A ship sends a signal out to determine the depth of the ocean. The signal returns 2,5 seconds later. If sound travels at 1450 m.s ${}^{-1}$ in sea water, how deep is the ocean at that point?

explain and give four Example hyperbolic function
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