Question

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

• A. 1, 2, 4
• B. 3, 4, 5
• C. 1,2,3,4
• D. All of these

Answer 1

Answer: (C)

The equation of travelling wave
$y=\frac{1}{10}\sin (60t+2x)$
Compare with the standard wave equation
$y=a\sin (\omega t+kx)$
we get
Amplitude, $a=\frac{1}{10}m=10cm$
Angular frequency, $\omega =60rad/s$ and
Angular wave number, $k=2rad/m$
$\therefore$ Velocity of the wave
$v=\frac{\omega }{k}=\frac{60}{2}=30m/s$
$\therefore$ 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.