Question

A vibrating tuning fork generates a wave given by $y=0.1\sin \pi (0.1x-2t)$ where $x$ and $y$ are in $\text{metre}$ and time $t$ in $\text{second}$. The distance travelled by the wave while the fork completes $25$ vibrations is

• A. $250\text{m}$
• B. $750\text{m}$
• C. $500\text{m}$
• D. $1000\text{m}$

Answer 1

The correct option is C $500\text{m}$

Equation of wave is
$y=0.1\sin \pi (0.1x-2t)$

from equation,
Angular wave number, $k=0.1\pi {\text{m}}^{-1}$
Angular frequency, $\omega =2\pi \text{rad/s}$

And we know that time period of wave is
$T=\frac{2\pi }{\omega }=\frac{2\pi }{2\pi }=1\text{s}$

So, total time $t$ in $25$ vibrations is
$t=25\times 1=25\text{s}$

Wave speed, $v=\frac{\omega }{k}=\frac{2\pi }{0.1\pi }=20\text{m/s}$

So, the distance travelled by the wave in $25\text{s}$ is

$d=vt=20\times 25=500\text{m}$

Hence, option $\left(b\right)$ is the correct answer.