NEET Physics Wave Mechanics NEET PYQ-Wave Mechanics

Two vibrating tuning forks produce progressive waves given by \[{{y}_{1}}=4\sin 500\,\pi t\] and \[{{y}_{2}}=2\sin \,506\,\pi t\]. Number of beats produced per minute is:                            [AIPMT (S) 2005]

A) 360

B)                  180

C) 3

D)                  60

Correct Answer: B

Solution :

Key Idea: To reach the solution the given wave equations must be compared with standard equation of progressive wave.

So,

\[{{y}_{1}}=4\sin 500\,\pi t\] (i)

\[{{y}_{2}}=2\sin 506\,\pi \,t\] (ii)

Comparing Eqs. (i) and (ii) with

\[y=a\sin \omega t\] (iii)

We have,

\[{{\omega }_{1}}=500\,\pi \]

\[\Rightarrow \] \[{{f}_{1}}=\frac{500\,\pi }{2\pi }=250\,beats/s\]

and \[{{\omega }_{2}}=506\,\pi \]

\[\Rightarrow \] \[{{f}_{2}}=\frac{506\,\pi }{2\pi }=253\,beats/s\]

Thus, number of beats produced

\[={{f}_{2}}-{{f}_{1}}=253-250\]

\[=3\,\text{beats}/s\]

\[=3\times 60\,\,beats/\min \]

\[=180\,beats/\min \]