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Q.

A string is clamped at both the ends, and it is vibrating in its 4^th harmonic. The equation of the stationary wave is $y = 0.3 \sin (0.157 x) \cos (200 π t)$ . The length of the string is
(all quantities are in SI units)

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a

80 m

b

40 m

c

60 m

d

20 m

answer is C.

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Detailed Solution

$\begin{array}{l} y = 0.3 \sin (0.157 x) \cos (200 π t) \\ c o m p a r i n g i t w i t h g e n e r a l e q u a t i o n o f s t a t i o n a r y \\ w a v e i . e y = a \sin k x \cos w t \\ k = (2 π / λ) = 0.157 \\ λ = \frac{2 π}{0.157} = 4 π^{2} (∴ \frac{1}{2 π} \approx 0.157) \\ ω = 200 π = \frac{2 π}{T} \Rightarrow T = \frac{1}{20} S \\ λ = \frac{2 l}{n} o r l = n (\frac{λ}{2}) \end{array}$

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