Waves

JEE Main level, single correct, medium

139 of 142

Question 139 of 142

When two sound waves travel in the same direction in a medium, the displacements of a particle located at ' xx ' at time ' tt ' is given by :
$\begin{aligned}
& y_1=0.05 \cos (0.50 \pi x-100 \pi t) \\
& y_2=0.05 \cos (0.46 \pi x-92 \pi t)
\end{aligned}$
where y1,y2y_1, y_2 and xx are in meters and tt in seconds.
The speed of sound in the medium is :

Show answer and solution

Answer: (B) 200 m/s200 \mathrm{~m} / \mathrm{s}

Standard equation
y(x,t)=Acos⁡(ωVx−ωt)y(x, t)=A \cos \left(\frac{\omega}{V} x-\omega t\right)
From any of the displacement equation
Say y1\mathrm{y}_1
ωV=0.50π\frac{\omega}{\mathrm{V}}=0.50 \pi and ω=100π\omega=100 \pi
∴100πV=0.5π\therefore \frac{100 \pi}{\mathrm{V}}=0.5 \pi
∴V=100π0.5π=200 m/s\therefore \mathrm{V}=\frac{100 \pi}{0.5 \pi}=200 \mathrm{~m} / \mathrm{s}

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