Question

The loudness of a sound is 8 dB when the amplitude of vibrations is 3 units. If the amplitude is increased to 12 units, find the loudness of the sound in dB.

• A.
  32
• B.
  8
• C. 64
• D. 128

Answer 1

The correct option is D 128

1. $Loudness\alpha Amplitud{e}^2$
Given,
Initial loudness of the sound = 8 dB
Initial amplitude of vibration = 3 unit
Final amplitude of vibration = 12 unit

Final amplidue is increased 4 times.
So, loudness is increased $4^2=16$ times
Therefore, final loudness= 16 x 8 = 128 dB