First slide

Speed of wave

Question

The equation of a transverse wave travelling on a rope is given by $y = 10 sinπ (0.01 x - 2.00 t)$ where y and x are in cm and t in seconds. The maximum transverse speed of a particle in the rope is about

Moderate

A

63 cm/s
B

75 cm/s
C

100 cm/s
D

121 cm/s

Solution

The given equation is y = $10 \sin π (0.01 πx - 2 πt)$
Hence $ω = coefficient of t = 2 π$
$\Rightarrow$ Maximum speed of the particle $v_{\max} = aω = 10 \times 2 π$
$= 10 \times 2 \times 3.14 = 6.28 = 63 cm / s$

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