Question 71: Waves

Question

Two waves $y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t)$ and $y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t)$ are travelling in a pipe placed along $x$-axis.

Accepted Answer

Number of times the intensity is maximum on superposition in 1 , is calculated as follows:
Here,
$$ \begin{aligned} y_1 & =\mathrm{A} \cos (0.5 \pi x-100 \pi t) \ y_1 & =\mathrm{A} \cos \left(\frac{2 \pi}{\lambda} x-2 \pi v_1 tight) \ y_2 & =\mathrm{A} \cos (0.46 \pi-92 \pi t) \ & =\mathrm{A} \cos \frac{2 \pi}{\lambda^2} x-2 \pi v_2 t \end{aligned} $$
The two waves travelling in same direction will form beats having frequency $=$ frequency of maximum
$$ =\mathrm{v}_1=\mathrm{v}_2=50-46=4 \mathrm{~Hz} 	ext { or } 4 \mathrm{~s}^{-1} . $$
$\left[ight.$ Here, $2 \pi v_1 t=100 \pi t$ and $2 \pi v_2 t=92 \pi, v_2=46 \mathrm{~Hz}$ ]

Answer

4

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6

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8

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10

Waves

Two waves y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t) and y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t) are travelling in a pipe placed along x-axis.

Choose the correct answer: