Wave Motion 1 Question 12

12. A wave is represented by the equation;

$$ y=A \sin (10 \pi x+15 \pi t+\pi / 3) $$

where, $x$ is in metre and $t$ is in second. The expression represents

(1990, 2M)

(a) a wave travelling in the positive $x$-direction with a velocity $1.5 m / s$

(b) a wave travelling in the negative $x$-direction with a velocity $1.5 m / s$

(c) a wave travelling in the negative $x$-direction with a wavelength $0.2 m$

(d) a wave travelling in the positive $x$-direction with a wavelength $0.2 m$

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Answer:

Correct Answer: 12. $(b, c)$

Solution:

  1. $\omega=15 \pi, k=10 \pi$

Speed of wave, $\quad v=\frac{\omega}{k}=1.5 m / s$

Wavelength of wave $\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{10 \pi}=0.2 m$

$10 \pi x$ and $15 \pi t$ have the same sign. Therefore, wave is travelling in negative $x$-direction.

$\therefore$ Correct options are (b) and (c).



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