MHT CET · Physics · Waves and Sound
The displacement of a wave travelling in the \(\mathrm{x}\) direction is \(\mathrm{y}=10^{-4} \sin [600 \mathrm{t}-2 \mathrm{x}+\pi / 3] \mathrm{m}\), where \(\mathrm{x}\) is in metre and \(\mathrm{t}\) in second. The speed of the wave is
- A \(200 \mathrm{~m} / \mathrm{s}\)
- B \(300 \mathrm{~m} / \mathrm{s}\)
- C \(600 \mathrm{~m} / \mathrm{s}\)
- D \(150 \mathrm{~m} / \mathrm{s}\)
Answer & Solution
Correct Answer
(B) \(300 \mathrm{~m} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
Velocity \(=\) Wavelength \(\times\) Frequency
Frequency \((f)=\frac{\omega}{2 \pi}=\frac{600}{2 \pi}\)
Wavelength \((\lambda)=\frac{2 \pi}{k}=\frac{2 \pi}{2}=\pi\)
Velocity \(=\pi \times \frac{600}{2 \pi}=300 \mathrm{~ms}^{-1}\)
Frequency \((f)=\frac{\omega}{2 \pi}=\frac{600}{2 \pi}\)
Wavelength \((\lambda)=\frac{2 \pi}{k}=\frac{2 \pi}{2}=\pi\)
Velocity \(=\pi \times \frac{600}{2 \pi}=300 \mathrm{~ms}^{-1}\)
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