Wave Motion 1 Question 8
8. A transverse wave is described by the equation $y=y _0 \sin 2 \pi\left(f t-\frac{x}{\lambda}\right)$. The maximum particle velocity is equal to four times the wave velocity if
(1984, 2M)
(a) $\lambda=\pi y _0 / 4$
(b) $\lambda=\pi y _0 / 2$
(c) $\lambda=\pi y _0$
(d) $\lambda=2 \pi y _0$
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Answer:
Correct Answer: 8. (b)
Solution:
- Wave velocity $v=\frac{\text { coefficient of } t}{\text { coefficient of } x}=\frac{2 \pi f}{2 \pi / \lambda}=\lambda f$
Maximum particle velocity $v _{p m}=\omega A=2 \pi f y _0$
Given,
$$ v _{p m}=4 v $$
$$ \text { or } \quad \begin{aligned} & 2 \pi f y _0 & =4 \lambda f \\ \therefore & \lambda & =\frac{\pi y _0}{2} \end{aligned} $$
