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Q. 76

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 454

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Short Answer

A loudspeaker on a pole is radiating 100 W of sound energy in all directions. You are walking directly toward the speaker at 0.80 m/s. When you are 20 m away, what are (a) the sound intensity level and (b) the rate (dB/s) at which the sound intensity level is increasing? Hint: Use the chain rule and the relationship log10 x = ln x/ln 10.

a) The intensity level of the sound source is 102.7 dB

b) The rate of increase in intensity level is 4.108 dB/s

See the step by step solution

Step by Step Solution

Step 1: Write the given information

The power of the sound source P= 100W

The speed of the listener v = 0.80m/s

The distance of the listener from the source is d = 20m

Step 2: (a) To determine the sound intensity level

The area covered by the sound source is 4πr2

Substitute the values

The intensity of the sound is

The sound intensity level is given by

Thus, the intensity level of the sound source is 102.7 dB

Step 3: (b) To determine the rate of increase in sound intensity level

The time taken by the sound to reach the listener is given by

In 25 seconds, the sound reaches the listener with an intensity level of 102.7 dB

The intensity level of sound in 1 sec is given by

Thus, the rate of increase in intensity level is 4.108 dB/s

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