Multiple choice

Sound from a source A is measured to be 20 dB, while that from a source B is measured to be 80 dB. If the amplitude of sound at A is a, then the amplitude of sound at B is

  1. 2a

  2. 4a

  3. 16a

  4. none of these
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A Correct answer
Explanation

Loudness of a sound is proportional to the square of its amplitude. Hence, let amplitude of the sound of 20 dB be a. Then, 20 = ka2; Sound of 80 dB = kb2 (where b is the amplitude of sound at B). i.e. 4ka2 = kb2 i.e. k(2a)2 = kb2 Hence, b = 2a. Thus, amplitude at B is double of that at A.

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