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Physics

The amplitude of a sound wave is reduced from 2 mm to 1 mm. The intensity of the sound will:

  1. become four times the initial
  2. remain the same
  3. become half of the initial
  4. become one fourth of the initial

Sound

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Answer

become one fourth of the initial

Reason

Given,

  • Initial amplitude = 2 mm
  • Final amplitude = 1 mm

As,

Intensity of a sound wave ∝ (Amplitude of vibrations)2

Then,

Final intensityInitial intensity=(Final amplitudeInitial amplitude)2=(12)2=14\dfrac{\text {Final intensity}}{\text {Initial intensity}} = \left({\dfrac{\text {Final amplitude}}{\text {Initial amplitude}}}\right)^2 = \left(\dfrac{1}{2}\right)^2 = \dfrac {1}{4}

So,

Final intensity = 14\dfrac {1}{4} x Initial intensity

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