Question

A wave equation which gives the displacement along the $y-$direction is given by $y={10}^{-4}\sin (60t+2x)$, where $x$ and $y$ are in $m$ and $t$ is time in seconds. This represents a wave.

• A. travelling with a velocity of $30m/s^{-1}$ in the negative $x-$direction.
• B. of wavelength $\pi m$.
• C. of frequency $30/\pi Hz$.
• D. of amplitude ${10}^{-4}m$ travelling along the negative $x-$direction.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A travelling with a velocity of $30m/s^{-1}$ in the negative $x-$direction.
B of wavelength $\pi m$.
C of frequency $30/\pi Hz$.
D of amplitude ${10}^{-4}m$ travelling along the negative $x-$direction.

$y={10}^{-4}\sin (60t+2x)$

1. $K=\frac{10}{V}\Rightarrow 2=-\frac{60}{V}\Rightarrow V=-30m/s$

2. $\frac{2I}{\lambda }=2\Rightarrow \lambda =\pi m$

3. $2\pi f=60\Rightarrow f=\frac{30}{\pi }Hz$

4. Amplitude = max(y)

${10}^{-1}m$