Wave Motion 1 Question 6
6. A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 cm / s$. The wavelength of the wave is $0.5 m$ and its amplitude is $10 cm$. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $5 cm$ is
(2008)
(a) $\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} m / s$
(b) $-\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} m / s$
(c) $\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} m / s$
(d) $-\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} m / s$
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Answer:
Correct Answer: 6. (a)
Solution:
- Particle velocity $v _p=-v$ (slope of $y-x$ graph)
Here, $v=+ve$, as the wave is travelling in positive $x$-direction.
Slope at $P$ is negative.
$\therefore$ Velocity of particle is in positive $y$ (or $\hat{\mathbf{j}}$ ) direction.
$\therefore$ Correct option is (a).
