A steel rod 100 cm long is clamped at its mid-point. funda-mental frequency of longitudinal vibratio

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14.Waves and Sound

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A steel rod $100 cm$ long is clamped at its mid-point. The funda-mental frequency of longitudinal vibrations of the rod is given to be $2.53 kHz$. What is the speed of sound in steel .... $km/s$

A

$5.06$

B

$6.06$

C

$7.06$

D

$8.06$

Solution

(a) If a rod clamped at middle, then it vibrates with similar fashion as open organ pipe vibrates as shown.

Hence, fundamental frequency of vibrating rod is given by ${n_1} = \frac{v}{{2l}}$

==> $2.53 = \frac{v}{{4 \times 1}}$

==> $v = 5.06 km/sec.$

Standard 11

Physics

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