MHT CET · Physics · Waves and Sound
The displacement of a particle in a medium is \(y=10^{-4} \sin \left[100 t+20 x+\frac{\pi}{3}\right] \mathrm{m}\), where \(t\) is in second and \(x\) is in metre. The speed of the wave is
- A \(5 \mathrm{~m} / \mathrm{s}\)
- B \(10 \mathrm{~m} / \mathrm{s}\)
- C \(15 \mathrm{~m} / \mathrm{s}\)
- D \(20 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(A) \(5 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
The equation can be written in the form of, \(y=y_0 \sin (\omega t+k x+\phi)\) where, \(\omega=100 / \mathrm{s}\) and \(k=20 / \mathrm{m}\)
The velocity of a travelling wave is given by, \(v=\omega / k\)
Hence, substituting the values, \(v=\frac{100}{20}=5 \mathrm{~m} / \mathrm{s}\)
The velocity of a travelling wave is given by, \(v=\omega / k\)
Hence, substituting the values, \(v=\frac{100}{20}=5 \mathrm{~m} / \mathrm{s}\)
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