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. $(a, b, c, d)$
Solution:
- $\omega=15 \pi, k=10 \pi$
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).
