A vibrating string of certain length ell under a tension mathrm{T} resonates with a mode correspondi

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14.Waves and Sound

hard

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

A

$344$

B

$336$

C

$117.3$

D

$109.3$

(IIT-2008)

Solution

$ \mathrm{n}_5=\frac{3}{4}\left(\frac{340}{0.75}\right)=\mathrm{n}-4 $

$ \therefore \mathrm{n}=344 \mathrm{~Hz}$

Standard 11

Physics

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