First slide

Speed of wave

Question

A transverse wave on a stretched string is represented by the equation $y = 0.4 \sin (60 t - 20 x),$ where x is in metre and t is in second. It linear mass density of the wire is $16 \times 10^{- 3} k g / m,$ the tension in the string is

Moderate

A

2.21 N
B

1.106 N
C

0.238 N
D

0.144 N

Solution

(4)
$\begin{array}{l} y = 0.4 \sin (60 t - 20 x) \\ ∴ V = V e l o c i t y o f p r o p a g a t i o n = \frac{ω}{k} = \frac{60}{20} m / s \\ \Rightarrow v = 3 m / s \\ N o w \sqrt{\frac{T}{μ}} = V \Rightarrow T = μ V^{2} (16 \times 10^{- 3}) \times 3^{2} N \\ \Rightarrow T_{c l o s e d} = 0.144 N \end{array}$

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