First slide

Stationary waves

Question

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is $y = 0.3 \sin (0.157 x) c o s (200 π t)$ . The length of the string is

Moderate

A

20 m
B

80 m
C

60 m
D

40 m

Solution

$I n c a s e o f 4 t h h a r m o n i c l = 4 \frac{λ}{2} \Rightarrow 2 λ = l P u t λ = \frac{2 π}{k} \Rightarrow \frac{4 π}{k} = l \Rightarrow l = \frac{4 π}{0.157} = 80 m$

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