Question

On sounding a string and a tuning fork simultaneously, six beats per second are produced if the length of the string is $95cm$ or $100cm$. The frequency of the fork is

• A. $117Hz$
• B. $234Hz$
• C. $4321Hz$
• D. $702Hz$

Answer 1

Answer: (B)

$234Hz$

Let the frequency of the tuning fork be ${\nu }^{\prime }$ and that of the string waves be $\nu$.

Thus $\nu =\frac{v}{2L}$ where $v$ is the velocity of the string waves

As beat frequency $b=|\nu -{\nu }^{\prime }|=6$

Now for $L=95cm=0.95m$, $\frac{v}{2\left(0.95\right)}-{\nu }^{\prime }=6$ ...........(1)

For $L=100cm=1m$, ${\nu }^{\prime }-\frac{v}{2\left(1\right)}=6$ ...........(2)

Adding (1) and (2) and solving $⟹v=456m/s$

Now from (1), $\frac{456}{2\left(0.95\right)}-{\nu }^{\prime }=6$

$⟹{\nu }^{\prime }=234Hz$