Question

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1.Suppose that a public address system emits sound uniformly in all directions and that there are no reflections. The intensity at a location 27 m away from the sound source is 3.0 × 10^-4 W/m². What is the intensity at a spot that is 74 m away?

2. A loudspeaker has a circular opening with a radius of 0.1224 m. The electrical power needed to operate the speaker is 25.4 W. The average sound intensity at the opening is 20.0 W/m². What percentage of the electrical power is converted by the speaker
into sound power?

3.Deep ultrasonic heating is used to promote healing of torn tendons. It is produced by applying ultrasonic sound over the affected area of the body. The sound transducer (generator) is circular with a radius of 1.16 cm, and it produces a sound intensity of 6.51 × 10³ W/m². How much time is required for the transducer to emit 4250 J of sound energy?

4.A woman stands a distance d from a loud motor that emits sound uniformly in all directions. The sound intensity at her position is an uncomfortable 3.3×10^-3 W/m². At a distance 3.7 times as far from the motor, what are (a) the sound intensity and (b) the sound intensity level relative to the threshold of hearing?

5. The volume control on a surround-sound amplifier is adjusted so the sound intensity level at the listening position increase from 26 to 68 dB. What is the ratio of the final sound intensity to the original sound intensity?

6. Using an intensity of 1 × 10^-12 W/m² as a reference, the threshold of hearing for an average young person is 0 dB. Person 1 and person 2, who are not average, have thresholds of hearing that are β₁ = -15.0 dB and β₂ = +8.00 dB. What is the ratio I₁/I₂ of the sound intensity I₁ when person 1 hears the sound at his own threshold of hearing compared to the sound intensity I₂ when person 2 hears the sound at his own threshold of hearing?

Answer 1

(1) Area of a sphere of radius r_o = 27 m is : 4r_o² = 4 x 3.14 x 27² m² = 9156.24 m².

Intensity of the sound at 27 m away is 3 × 10^-4 W / m².

Hence, power of the source = P = Intensity x Area = 3 × 10^-4 W / m² x 9156.24 m² ~ 2.747 W.

Now, area of a sphere of radius r = 74 m is : 4r² = 4 x 3.14 x 74² m² = 68778.56 m².

Hence, the intensity at a spot, that is 74 m away from the sound source, is :

P / 4r² = 2.747 W /  68778.56 m² ~ 4 x 10^-5 W / m².