Question

Two waves have amplitude ratio 1:3 what is the ratio of their intensities

Answer 1

Two waves have amplitude ratio 1:3, the ratio of their intensities is 1:9

Given, the ratio of the amplitudes of two waves are 1:3.

So, if two waves are A and B, then the

Amp. of A / Amp. of B = 1 / 3

We know that the intensity of a wave is proportional to its amplitude.

So, for A and B, the

Intensity of A / Intensity of B = (1)² / (3)² = 1 / 9.

Thus, the required ratio of intensities is equal to 1:9.

Answer 2

The ratio of their intensities are 1:9.

Explanation:

Given that,

Ratio of amplitude of the waves= 1:3

We know that,

The intensity of the wave is directly proportional to the square of the amplitude of the wave.

$I\propto A^2$

We need to calculate the ratio of their intensities

Using formula of intensity

$\dfrac{I}{I'}=\dfrac{A^2}{A'^2}$

Where, I = intensity of first wave

I'= intensity of second wave

A = amplitude of first wave

A'= amplitude of second wave

Put the value into the formula

$\dfrac{I}{I'}=\dfrac{1^2}{3^2}$

$\dfrac{I}{I'}=\dfrac{1}{9}$

Hence, The ratio of their intensities are 1:9.

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Topic : intensity

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