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Problem: If the amplitude of a sound wave is tripled, (a) by what factor will the intensity increase? (b) By how many dB will the sound level increase?

FREE Expert Solution

The intensity of a sound wave:

I=2π2vρf2A2

For a given wave, the velocity, density, and frequency are the same.

Therefore, intensity, I is directly proportional to A2.

(a)

Given that I1 and I2 are the intensities of the sound wave and A1 and A2 are the amplitudes, then we have:

I1/I2 = (A1/A2)2 

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Problem Details

If the amplitude of a sound wave is tripled, (a) by what factor will the intensity increase? (b) By how many dB will the sound level increase?

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