Wave Motion 1 Question 13
13. A wave equation which gives the displacement along the $y$-direction is given by : $y=10^{-4} \sin (60 t+2 x)$ where, $x$ and $y$ are in metre and $t$ is time in second. This represents a wave
(1981, 3M)
(a) travelling with a velocity of $30 m / s$ in the negative $x$-direction
(b) of wavelength $(\pi) m$
(c) of frequency $\left(\frac{30}{\pi}\right) Hz$
(d) of amplitude $10^{-4} m$
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Answer:
Correct Answer: 13. $(a, b, c, d)$
Solution:
- $y=10^{-4} \sin (60 t+2 x)$
$A=10^{-4} m, \omega=60 rad / s, k=2 m^{-1}$
Speed of wave, $\quad v=\frac{\omega}{k}=30 m / s$
Frequency, $f=\frac{\omega}{2 \pi}=\frac{30}{\pi} Hz$.
Wavelength $\lambda=\frac{2 \pi}{k}=\pi m$
Further, $60 t$ and $2 x$ are of same sign. Therefore, the wave should travel in negative $x$-direction.
$\therefore$ All the options are correct.
