Question

A travelling wave is represented by the equation $y=\frac{1}{10} \sin (60 t+2 x)$, where $x$ and $y$ are in meter and $t$ is in second. This represents a wave 1. travelling with a velocity of $30\, ms ^{-1}$ 2. of frequency $\frac{30}{\pi} Hz$ 3. of wavelength $\pi$ meter 4. of amplitude $10\, cm$ 5. moving in the positive $x$-direction Pick out the correct statements from the above.

• A. 37988
• B. 38415
• C. 1,2,3,4
• D. All of these

Answer 1

Answer: (C)

1,2,3,4

Answer 2

The equation of travelling wave
$y=\frac{1}{10} \sin (60\, t+2\, x)$
Compare with the standard wave equation
$y=a \sin (\omega t+ k x)$
we get
Amplitude, $a=\frac{1}{10} m =10\, cm$
Angular frequency, $\omega=60\, rad / s$ and
Angular wave number, $k=2\, rad / m$
$\therefore$ Velocity of the wave
$v=\frac{\omega}{k}=\frac{60}{2}=30\, m / s$
$\therefore$ Frequency of the wave
$f=\frac{\omega}{2 \pi}=\frac{60}{2 \pi}=\frac{30}{\pi} H$
Wavelength of the wave
$\lambda=\frac{2 \pi}{k}=\frac{2 \pi}{2}=\pi m$
There is positive sign between $t$ and $x$ terms, the given wave is moving in the negative $x$-direction.