First slide

Stationary waves

Question

A string is rigidly tied at two ends and its equation of vibration is given by $y = \cos 2 π t \sin 2 πx .$ Then minimum length of string is

Moderate

A

1 m
B

$\frac{1}{2} m$
C

5 m
D

$2 π m$

Solution

Given equation of stationary wave is
$y = \sin 2 πx \cos 2 πt$ , comparing it with standard equation $y = 2 Asin \frac{2 πx}{λ} \cos \frac{2 π v t}{λ}$
We have $\frac{2 πx}{λ} = 2 πx \Rightarrow λ = 1 m$
Minimum distance of string (first mode) $L_{\min} = \frac{λ}{2} = \frac{1}{2} m$

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