Question

A wave of amplitude 20mm has intensity Ix. Another wave of the same frequency but of amplitude 5mm has an intensity Iy.

Answer 1

Answer:

(C) 16

Explanation:

Given:

The amplitude of first wave (s₁) = 20 mm

The amplitude of second wave (s₂) = 5 mm

Intensity of first wave = Iₓ

Intensity of second wave = $I_y$

The intensity associated with a wave depends on the amplitude of the wave.

The intensity (I) is directly proportional to the square of the amplitude (s) of the wave and is expressed as:

$I=ks^2\\Where\ k\to constant\ of\ proportionality$

Now, the intensities of the two waves are given as:

$I_x=ks_1^2=k(20)^2\\\\I_y=ks_2^2=k(5)^2$

Dividing both the intensities, we get:

$\frac{I_x}{I_y}=\frac{k(20)^2}{k(5)^2}\\\\\frac{I_x}{I_y}=\frac{400}{25}\\\\\frac{I_x}{I_y}=16$

Therefore, the option (C) is correct.