First slide

Travelling wave

Question

The displacement y (in cm) produced by a simple harmonic wave is $y = \frac{10}{π} \sin (2000 πt - \frac{πx}{17})$ . The periodic time and maximum velocity of the particles in the medium will respectively be

Moderate

A

10^-3 sec and 330 m/sec
B

10^-4 sec and 20 m/sec
C

10^-3 sec and 200 m/sec
D

10^-2 sec and 2000 m/sec

Solution

Comparing with $y = asin (ωt - kx) \Rightarrow a = \frac{10}{π}, ω = 200 π$
$∴ v_{\max} = aω = \frac{10}{π} \times 2000 π = 200 m / \sec$
and $ω = \frac{2 π}{T} \Rightarrow 200 π = \frac{2 π}{T} \Rightarrow T = 10^{- 3} \sec$

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