question_answer

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           [AFMC 2000]

A)            5.06 km/s                              

B)            6.06 km/s

C)            7.06 km/s                              

D)            8.06 km/s

Correct Answer: A

Solution :

                     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 \[{{n}_{1}}=\frac{v}{2l}\]Þ \[2.53=\frac{v}{4\times 1}\]Þ v = 5.06 km/sec.