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What is the beat frequency produced when following two waves are sounded together ?x1 = 10 sin (404πt – 5πx),x2 = 10 sin (400πt – 5πx).     4132

Question

What is the beat frequency produced when following two waves are sounded together?

x1=10sin(404πt5πx) x_1 = 10 \sin(404\pi t - 5\pi x)
x2=10sin(400πt5πx) x_2 = 10 \sin(400\pi t - 5\pi x)

4132

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Solution

The beat frequency is produced by the interference of two waves of different frequencies. It is calculated by taking the absolute difference of the two frequencies.

The frequency of a wave is given by the coefficient of 't' in the equation of the wave.

For the first wave, x1 = 10 sin (404πt – 5πx), the frequency is 404/2 = 202 Hz (since 2πf is the coefficient of 't', where f is the frequency).

For the second wave, x2 = 10 sin (400πt – 5πx), the frequency is 400/2 = 200 Hz.

Therefore, the beat frequency is |202 Hz - 200 Hz| = 2 Hz.

This problem has been solved

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