Waves

JEE Main level, single correct, medium

43 of 142

Question 43 of 142

A transverse wave is represented by : y=10πsin(2πTt−2πλx)\text{y}=\dfrac{10}{\pi }sin\left(\dfrac{2\pi }{\text{T}}\text{t}-\dfrac{2\pi }{\lambda }\text{x}\right) For what value of the wavelength the wave velocity is twice the maximum particle velocity?

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Answer: (A) 40 cm

wavevelocity=nλwavevelocity=n\lambda

(Vp)max=aω{({V}_{p})}_{max}=a\omega

nλ=2a(2πn)n\lambda =2a\left(2\pi n\right)

λ=2(a)2π\lambda =2(a)2\pi

=2.10π.2π=2.\dfrac{10}{\pi }.2\pi

= 40 cm

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