Q. 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
A) $5.06\ km/s$
B) $6.06\ km/s$
C) $7.06\ km/s$
D) $8.06\ km/s$
Explanation
(a) If a rod champed at middle, then it vibrates with similar fashion as open organ pipe vibrates as shown.
Hence, fundamental frequency of vibrating rod is given by
$n_{1} = \frac{v}{2l} \Rightarrow 2.53 = \frac{v}{2 \times 1} \Rightarrow v = 5.06\ km/sec$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.