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  • Help me understand! A steel rod 100 cm long is clamped at its midpoint. The fundamental frequency of longitudinal vibrations of the rodis given to be 2.53 KHz. What is the speed of sound on steel

A steel rod 100 cm long is clamped at its midpoint. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 KHz. What is the speed of sound on steel

  • Option 1)

    5.06 km/s

  • Option 2)

    6.06 km/s

  • Option 3)

    7.06 km/s

  • Option 4)

    8.06 km/s

 

Answers (1)

best_answer

It rod is clamped at middle

it vibrate like open organ pipe

n_{1}= \frac{v}{2l} \Rightarrow \frac{v}{2\times 1} \Rightarrow v= 5.06 km/s

 

Vibration of composite string when joint act as antinode -

\frac{2n_{1}-1}{2n_{2}-1}= \frac{\lambda _{2}l_{1}}{\lambda _{1}l_{2}}= \frac{l_{1}}{l_{2}}\cdot \sqrt{\frac{\mu _{1}}{\mu _{2}}}

n_{1}\: and \; n_{2} are number of loops

l_{1}\: and \; l_{2} are length of two parts

\mu _{1}\: and \; \mu _{2} are linear density in two parts

-

 

 


Option 1)

5.06 km/s

This is correct

Option 2)

6.06 km/s

This is incorrect

Option 3)

7.06 km/s

This is incorrect

Option 4)

8.06 km/s

This is incorrect

Posted by

prateek

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