Two sound waves having displacements x_1 = 2 | vedclass

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(C) Given equations of displacement are:$x_1 = 2 \sin(1000 \pi t)$$x_2 = 3 \sin(1006 \pi t)$Comparing these with the standard equation $x = A \sin(\om

Vedclass · Accepted Answer

$3$ beats/s with maximum intensity $25$ units

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(C) Given equations of displacement are:$x_1 = 2 \sin(1000 \pi t)$$x_2 = 3 \sin(1006 \pi t)$Comparing these with the standard equation $x = A \sin(\omega t)$,we get:Angular frequencies: $\omega_1 = 1000 \pi$ and $\omega_2 = 1006 \pi$.Amplitudes: $A_1 = 2$ and $A_2 = 3$.The frequencies are $f_1 = \frac{\omega_1}{2 \pi} = \frac{1000 \pi}{2 \pi} = 500 	ext{ Hz}$ and $f_2 = \frac{\omega_2}{2 \pi} = \frac{1006 \pi}{2 \pi} = 503 	ext{ Hz}$.Beat frequency is given by $|f_2 - f_1| = |503 - 500| = 3 	ext{ beats/s}$.Maximum intensity is proportional to the square of the maximum amplitude $(A_{	ext{max}} = A_1 + A_2)$.$A_{	ext{max}} = 2 + 3 = 5$ units.Maximum intensity $\propto (A_{	ext{max}})^2 = (5)^2 = 25$ units.Therefore,the waves produce $3$ beats/s with a maximum intensity of $25$ units.

Two sound waves having displacements $x_1 = 2 \sin(1000 \pi t)$ and $x_2 = 3 \sin(1006 \pi t)$,when interfere,produce

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