A vibrating string of certain length l under a tension T reasonat… - Vidyadip

MCQ

A vibrating string of certain length $l$ under a tension $T$ reasonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75$ $cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. 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 $340$ $m/s$, the frequency $n$ of the tuning fork in $Hz $ is

✓
$344$
B
$336$
C
$117.3$
D
$109.3$

✓

Answer

Correct option: A.

$344$

a
$n = \frac{{3v}}{{4l}} = \frac{{3 \times 340}}{{4 \times \frac{{75}}{{100}}}} = 340{\mkern 1mu} {\rm{\,Hz}}$

Shring Fork Beats

$340$ $344$ or $336$ $4$

$T \uparrow $ $2$

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