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Perception of Sound

The loudness ...

Question

The loudness of a sound is 8 dB when the amplitude of vibrations is 2 units. If the amplitude is increased to 8 units, find the loudness of the sound in dB.

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Solution

$L o u d n e s s \propto {(A m p l i t u d e)}^{2}$
Here amplitude is increased by 4 times. So, loudness should increase by 16 times.
Therefore, loudness $= 16 \times 8 = 128 d B$

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