Question:
A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by
\(y(x,t) = 0.5\sin\left(\frac{5\pi}{4}x\right)\cos(200\pi t)\).
What is the speed of the travelling wave moving in the positive \(x\) direction ?
(\(x\) and \(t\) are in meter and second, respectively.)
A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by
\(y(x,t) = 0.5\sin\left(\frac{5\pi}{4}x\right)\cos(200\pi t)\).
What is the speed of the travelling wave moving in the positive \(x\) direction ?
(\(x\) and \(t\) are in meter and second, respectively.)
\(y(x,t) = 0.5\sin\left(\frac{5\pi}{4}x\right)\cos(200\pi t)\).
What is the speed of the travelling wave moving in the positive \(x\) direction ?
(\(x\) and \(t\) are in meter and second, respectively.)
Show Hint
A standing wave y = 2A sin(kx) cos(wt) is made of two travelling waves with the same k and omega; the speed is omega / k.
Updated On: Nov 11, 2026
- \(160\ \mathrm{m/s}\)
- \(90\ \mathrm{m/s}\)
- \(180\ \mathrm{m/s}\)
- \(120\ \mathrm{m/s}\)
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The Correct Option is A
Solution and Explanation
The standing wave \(y = 2a\sin kx\cos\omega t\) is the sum of \(a\sin(kx - \omega t)\) and \(a\sin(kx+\omega t)\), so each travelling wave has the same \(k\) and \(\omega\).
Comparing: \(k = \frac{5\pi}{4}\ \mathrm{m^{-1}}\), \(\omega = 200\pi\ \mathrm{rad/s}\).
\(v = \frac{\omega}{k} = \frac{200\pi}{5\pi/4} = 200\times\frac{4}{5} = 160\ \mathrm{m/s}\)
Answer: (1) \(160\ \mathrm{m/s}\)
Comparing: \(k = \frac{5\pi}{4}\ \mathrm{m^{-1}}\), \(\omega = 200\pi\ \mathrm{rad/s}\).
\(v = \frac{\omega}{k} = \frac{200\pi}{5\pi/4} = 200\times\frac{4}{5} = 160\ \mathrm{m/s}\)
Answer: (1) \(160\ \mathrm{m/s}\)
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