1. Tardigrade
  2. Question
  3. Physics
  4. When two sound waves travel in the same direction in a medium, the displacements of a particle located at 'x' at time 't' is given by: y1 = 0.05 cos (0.50 π x -100 π t) y2 = 0.05 cos (0.46 π x - 92 π t) where y1, y2 and x are in meters and t in seconds. The speed of sound in the medium is :

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Q. When two sound waves travel in the same direction in a medium, the displacements of a particle located at $'x'$ at time $'t'$ is given by :
$y_{1} = 0.05 \,cos \left(0.50\, \pi x -100 \,\pi t\right)$
$y_{2} = 0.05 \,cos \left(0.46\, \pi x - 92 \,\pi t\right)$
where $y_1, \,y_2$ and $x$ are in meters and $t$ in seconds. The speed of sound in the medium is :

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Solution:

Standard equation
$y \left(x, t\right) = A\,cos \left(\frac{\omega}{V}x - \omega t\right)$
From any of the displacement equation Say $y_{1}$
$\frac{\omega}{V} = 0.05\pi and \omega = 100\pi$
$\therefore \frac{100\pi}{V} = 0.5\pi$
$\therefore V = \frac{100\pi}{0.5\pi} =200m/s$