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Intensity of sound (not included in caps - advanced)

Advanced section

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 is defined as:

Intensity = energy time × area = power area

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

Joules s · m 2 = Watts m 2

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

The average threshold of hearing is 10 - 12 W · m - 2 . Below this intensity, the sound is too soft for the ear to hear. The threshold of pain is 1 . 0 W · 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:

β = 10 log I I o I o = 10 - 12 W · m - 2

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

Examples of sound intensities.
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.


  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 m · 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.


  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
  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 200 Hz
    2. 2 Hz 2 000 Hz
    3. 20 Hz 20 000 Hz
    4. 200 Hz 200 000 Hz
    5. 2 000 Hz 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 m · s - 1 , what will be the time interval between the two loudest echoes?
    1. 2 3 s
    2. 1 6 s
    3. 5 6 s
    4. 1 s
    5. 1 3 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 m · 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. 1 9 the velocity of the first wave.
    2. 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 m · 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?

Questions & Answers

explain and give four Example hyperbolic function
Lukman Reply
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
on number 2 question How did you got 2x +2
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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
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Harshika Reply
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Shirley Reply
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find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
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use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
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Seidu Reply
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Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
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Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Need help solving this problem (2/7)^-2
Simone Reply
what is the coefficient of -4×
Mehri Reply
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Alfred Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
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how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Source:  OpenStax, Physics - grade 10 [caps 2011]. OpenStax CNX. Jun 14, 2011 Download for free at http://cnx.org/content/col11298/1.3
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