Question

Two vibrating tuning forks produce progressive waves given by $y_1=4sin$ 500 $\pi t$ and $y_2=2$ sin $505$$\pi t$. Number of beat produced per minute is

• A. 360
• B. 180
• C. 3
• D. 60

Answer 1

The correct option is B 180

$y_1=4sin500\pi t$

$y_2=2sin506\pi t$

Comparing the above equations,

$y=asin\omega t$

We have,

${\omega }_1=500\pi$

$⟹f_1=\frac{500\pi }{2\pi }$

$⟹f_1=250beats/s$

and ${\omega }_2=506\pi$

$f_2=\frac{506\pi }{2\pi }$

$f_2=253beats/s$

Thus, number of beats produced

$=f_2-f_1$

$=253-250$

$=3beats/s=3\times 60beats/min$

So, Number of beats $=180beats/min$