Worksheet: Sound Wave Power and Intensity

In this worksheet, we will practice relating sound intensity level in decibels to sound wave intensity, amplitude, and pressure changes that waves produce.


The energy of a ripple on a pond is proportional to the amplitude squared. If the amplitude of the ripple is 0.100 cm at a distance from the source of 6.0 meters, what was the amplitude at a distance of 2.0 meters from the source?


The low-frequency speaker of a stereo set has a surface area of 𝐴=0.05m and produces 1 W of acoustical power.

What is the intensity at the speaker?

If the speaker projects sound uniformly in all directions, at what distance from the speaker is the intensity 0.1 W/m2?


A microphone receiving a pure sound tone is connected to an oscilloscope, producing a wave on its screen. The sound intensity is originally 2.00×10 mW/m2 but is increased until the amplitude shown by the oscilloscope increases by 30.00%. What is the intensity of the sound after the amplitude increases?

  • A2.60×10 W/m2
  • B3.38×10 W/m2
  • C4.22×10 W/m2
  • D2.30×10 W/m2
  • E3.82×10 W/m2


Ten cars in a circle at a boom box competition produce a 120 dB sound intensity level at the center of the circle. What is the average sound intensity level produced there by each stereo, assuming interference effects can be neglected?


If a woman needs an amplification of 6.3×10 times the threshold intensity to enable her to hear at all frequencies, what is her overall hearing loss in decibels?


A tuning fork of frequency 250 Hz is struck. The sound intensity at a distance of 1.00 m from the fork is 𝐼 W/m2.

What is the sound intensity in terms of 𝐼 at a distance of 4.00 m from the fork?

  • A0.0448𝐼
  • B0.0229𝐼
  • C0.0625𝐼
  • D0.134𝐼
  • E0.132𝐼

At what distance from fork is the sound intensity 0.100𝐼 W/m2?


A sound wave in air producing a sound level of 0 dB at a frequency of 1,000 Hz corresponds to a maximum gauge pressure of 10 atm.

What is the maximum gauge pressure if the sound level is 60 dB?

  • A10 atm
  • B10 atm
  • C10 atm
  • D10 atm
  • E10 atm

What is the maximum gauge pressure if the sound level is 120 dB?

  • A10 atm
  • B10 atm
  • C10 atm
  • D10 atm
  • E10 atm


Suppose that the sound level from a source is 75.0 dB and then drops to 52.0 dB, with a frequency of 600 Hz. The air temperature is 24.0C and the air density is 1.184 kg/m3.

Determine the initial sound intensity.

Determine final sound intensity.

Determine the initial sound wave amplitude.

Determine the final sound wave amplitude.


Sound is more effectively transmitted by solid substances than through the air, and perceived sound is intensified if it is concentrated onto the small area of the eardrum. Sound is transmitted into a stethoscope 100 times as effectively as transmitted though air. What is the gain in decibels produced by a stethoscope that has a sound gathering area of 15.0 cm2 and concentrates the sound onto two eardrums with a total area of 0.900 cm2, with an efficiency of 40.0%?


A sound has a level of 90.0 dB.

What is the decibel level of a sound that is twice as intense?

What is the decibel level of a sound that is one-fifth as intense?


What is the intensity of a sound that has a level 4.00 dB lower than a sound of intensity 7.00×10 W/m2?

  • A3.00×10 W/m2
  • B4.79×10 W/m2
  • C2.79×10 W/m2
  • D4.00×10 W/m2
  • E3.79×10 W/m2


An exposure to a sound intensity level of 170 dB for 18×10 s may cause hearing damage. What energy in joules is transmitted to an eardrum of diameter 0.600 cm exposed to such a dose of sound?

  • A34×10 J
  • B51×10 J
  • C9.0×10 J
  • D17×10 J
  • E65×10 J


The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound intensity level goes up by 25.0 dB?


The threshold of human hearing is approximately −8.00 dB. What is the intensity of a sound at this level? (Take the threshold intensity of hearing is 𝐼=1.00×10/Wm)

  • A1.44×10 W/m2
  • B1.32×10 W/m2
  • C1.24×10 W/m2
  • D1.58×10 W/m2
  • E1.70×10 W/m2


A sound wave traveling in air has a pressure amplitude of 0.35 Pa. Find the intensity of the wave. Use a value of 343 m/s for the speed of sound. Take the density of the air to be 1.225 kg/m3.

  • A1.5×10 W/m2
  • B2.9×10 W/m2
  • C1.5×10 W/m2
  • D2.9×10 W/m2
  • E4.2×10 W/m2


A person has a hearing threshold 10 dB above normal at 100 Hz and 50 dB above normal at 4,000 Hz. How many times more intense must a 100 Hz tone be than a 4,000 Hz tone if they are both barely audible to this person?


What is the sound intensity level produced by earphones that create an intensity of 3.29×10 W/m2?


What is the intensity of a 145 dB sound?


If a large housefly that is 4.0 m away from you makes a 30.0 dB noise, what is the noise level of 1,000 flies at a 4.0 m distance, assuming interference has a negligible effect?


The warning tag on a lawn mower states that it produces noise at a level of 91.0 dB. What is this in watts per meter squared?

  • A1.50×10 W/m2
  • B1.66×10 W/m2
  • C1.26×10 W/m2
  • D1.80×10 W/m2
  • E1.11×10 W/m2


Loudspeakers can produce intense sounds with surprisingly small energy input in spite of their low efficiencies. What is the power input needed to produce a 110.0 dB sound intensity level for a 6.000-centimeter-diameter speaker that has an efficiency of 5.00%?

  • A5.78×10 W
  • B5.66×10 W
  • C5.66×10 W
  • D5.66×10 W
  • E4.73×10 W


Ultrasound of intensity 2.30×10 W/m2 is produced by the rectangular head of a medical imaging device measuring 4.00 cm by 7.00 cm. What is its power output?


A 2.50 m diameter university communications satellite dish receives TV signals that have a maximum electric field strength of 7.50 µV/m for one channel.

What is the intensity of this wave?

  • A7.54×10 W/m2
  • B7.47×10 W/m2
  • C7.26×10 W/m2
  • D7.40×10 W/m2
  • E7.33×10 W/m2

What is the power received by the antenna?

  • A4.23×10 W
  • B3.66×10 W
  • C3.21×10 W
  • D4.50×10 W
  • E3.90×10 W

If the orbiting satellite broadcasts uniformly over an area of 1.50×10 m2 (a large fraction of North America), how much power does it radiate?


A sound wave traveling in air has a pressure amplitude of 0.50 dB. What intensity level does this correspond to?

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