Question

Two waves of equal frequencies are superimposed on each other if the maximum intensity is 16 times of the minimum intensity what is ratio of their amplitudes

Answer 1

Answer: The ratio of the amplitudes is 4:1.

Explanation:

Given that,

Maximum intensity is 16 times of the minimum intensity.

$I_{max}=16 I_{min}$

We know that,

Intensity of the wave is directly proportional to the square of the amplitude.

$I \propto a^2$

$\dfrac{I_{max}}{I_{min}}=(\dfrac{a_{max}}{a_{min}})^2$.....(I)

Put the value of $I_{max}$ in equation (I)

$\dfrac{16I_{min}}{I_{min}}=(\dfrac{a_{max}}{a_{min}})^2$

$\sqrt{\dfrac{16}{1}} = \dfrac{a_{max}}{a_{min}}$

$\dfrac{a_{max}}{a_{min}}=\dfrac{4}{1}$

Hence, The ratio of the amplitudes is 4:1.

Answer 2

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