Waves

JEE Main level, single correct, medium

59 of 142

Question 59 of 142

A string is clamped at both the ends and it is vibrating in its 4th{4}^{th} harmonic. The equation of the stationary wave is y=0.3sin⁡⁡(0.157x)cos(200πt)y=0.3\sin ⁡\left(0.157x\right)cos(200\pi t). The length of the string is
(All quantities are in SISI units.)

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Answer: (D) 80m80m

From the equation, k=0.157k=0.157
2πλ=0.157\dfrac{2\pi }{\lambda }=0.157
λ=40m\lambda =40m
But, length of the wire in 4th{4}^{th} harmonic, l=4×λ2=2λ=80ml=4\times \dfrac{\lambda }{2}=2\lambda =80m.

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