Question

A vibrating string of certain length $\ell$ under a tension $T$ resonates with a mode corresponding to the first overtone of an air column of length $75cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased, the number of beats reduces to $2$ per second. Assuming the velocity of sound in air to be $340m/s$, the frequency $n$ of the tuning fork in $Hz$ is.

• A. $344$
• B. $336$
• C. $117.3$
• D. $109.3$

Answer 1

Answer: (A)

$344$

The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$.
The beat frequency is given by: $f_{beat}=f_{string}\pm f_{tuningfork}$.

Now, 1st overtone of an air column of length $75cm$ inside a tube closed at one end is $340Hz.$
Now when the tension of the string is slightly increased, the number of beats reduces to $2$ per second. So, the frequency $n$ of the tuning fork is $340+4=344Hz$.