Worksheet: Loudness

In this worksheet, we will practice determining the frequencies of sound waves as measured by observers moving relative to the sources of the sounds.

Q1:

The sound of a vacuum cleaner has an intensity at the position of the ear of the person using the cleaner of 17.5 µW/m2. What is the loudness of the sound?

Q2:

The intensity of a sound wave is related to the velocity of the sound wave and the pressure at a point in the medium that the sound wave moves through.

Would an increase in the velocity of a sound wave increase or decrease the intensity of the sound wave?

  • ADecrease
  • BIncrease

Would an increase in the pressure at a point in the medium that the sound wave moves through increase or decrease the intensity of the sound wave?

  • ADecrease
  • BIncrease

Q3:

The intensity of a sound wave is the average power in the wave per unit area that the wave is incident on. Which of the following is the base SI unit that corresponds to the ratio of power to area?

  • A kg/s3
  • B kg/s2
  • C kg⋅m/s2
  • D kg⋅m/s3
  • E kg/m⋅s2

Q4:

Which of the following statements correctly describes the relationship between loudness in decibels and loudness in phons?

  • ALoudness in phons is equal to the ratio of loudness in decibels to sound frequency.
  • BLoudness in phons is equal to the ratio of the sound frequency to the loudness in decibels.
  • CLoudness in phons is equal to the ratio of the sound wave intensity to the sound frequency.
  • DLoudness in phons is equal to loudness in decibels for a sound frequency of 1 kHz.
  • ELoudness in phons is equal to the ratio of the sound frequency to the sound wave intensity.

Q5:

The sound of a voice emitted from the speaker of a mobile phone has an intensity at the position of the ear of the person holding the phone of 1.0 µW/m2. What is the loudness of the sound?

Q6:

What is the intensity, in watts per square meter, of the threshold of human hearing for sounds of a frequency of 1 kHz?

  • A 1 0 W/m2
  • B 1 0 W/m2
  • C 1 0 W/m2
  • D 1 0 W/m2
  • E 1 W/m2

Q7:

The intensity of a sound wave is related to the maximum displacement of particles of the medium that the sound wave moves through from their equilibrium positions. The displacement of two particular particles is shown by the red lines in the diagram. The particles are at their equilibrium positions when no wave is traveling through the medium.

Would an increase in the maximum displacement of a particle of the medium that the sound wave moves through increase, decrease, or have no effect on the intensity of the sound wave?

  • ANo effect
  • BDecrease
  • CIncrease

Would a decrease in the frequency of the sound wave increase, decrease, or have no effect on the intensity of the sound wave?

  • ANo effect
  • BIncrease
  • CDecrease

Would an increase in the density of the medium that the sound wave moves through increase, decrease, or have no effect on the intensity of the sound wave?

  • ADecrease
  • BNo effect
  • CIncrease

Q8:

The intensities of two sound waves at a point are 25 mW/m2 and 150 mW/m2. What is the difference between the loudness produced by the higher-intensity sound wave and the loudness produced by the other sound wave?

  • A 3.9 dB
  • B 7.8 dB
  • C 31 dB
  • D 23 dB
  • E 38 dB

Q9:

A woman and her dog are in a garden while a jet airplane flies over. The dog barks at the jet. At the position of the woman’s ear, the bark has a loudness of 72 dB and the jet noise has a loudness of 105 dB. What is the ratio of the intensity of the sound waves produced by the jet noise to the intensity of the sound waves produced by the bark?

  • A53
  • B33
  • C5
  • D 1,100
  • E 2,000

Q10:

The loudness of two sounds at a point are 120 dB and 90 dB. What is the ratio of the intensity of the sound wave producing the louder sound to the intensity of the sound wave producing the other sound?

Q11:

The loudness of two sounds at a point are 45 dB and 42 dB. What loudness value results from combining these two sounds?

Q12:

A sound wave produced by an alarm has a loudness of 80 dB at the position of the ear of a person sleeping in bed. What is the intensity of the sound wave in watts per square meter at this position?

  • A 1 0 W/m2
  • B 8 × 1 0 W/m2
  • C 8 × 1 0 W/m2
  • D 1 0 W/m2
  • E 1 0 W/m2

Q13:

An ambulance siren has a loudness of 115 dB at the position of the ear of a person hearing the ambulance drive past them. What is the intensity of the sound wave in watts per square meter at this position?

Q14:

The intensities of two sound waves at a point are 50 µW/m2 and 500 µW/m2. What is the difference between the loudness of the higher-intensity sound and the loudness of the other sound?

Q15:

Which of the following formulas correctly relates the intensity 𝐼 in watts per square meter of a sound to the threshold of human hearing, 𝐼 , and 𝐿 , the loudness of the sound in decibels (dB)?

  • A 𝐿 = 𝐼 𝐼 l o g
  • B 𝐿 = 1 0 𝐼 𝐼 l o g
  • C 𝐿 = 𝐼 𝐼 l o g
  • D 𝐿 = 1 0 l o g
  • E 𝐿 = 1 0 𝐼 𝐼 l o g

Q16:

How many 55 dB sound sources would have to be combined to have a loudness of 110 dB? Round to the nearest whole number of sounds.

  • A100
  • B562
  • C 316,228
  • D6
  • E 5,750

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