A steel bar of length 200 cm is nailed at its midpoint. The fundamental frequency of the longitudinal vibrations of the rod is 2.53 kHz. At what speed will the sound be able to travel through steel?

Asked by Pragya Singh | 1 year ago |  138

1 Answer

Solution :-

Length , l = 200 cm = 2 m
Fundamental frequency of vibration, 

νF = 2.53 kHz = 2.53 × 103 Hz

The bar is then plucked at its midpoint, forming an antinode (A) at its centre, and nodes (N) at its two edges, as depicted in the figure below :

The distance between two successive nodes is \( \dfrac{λ}{2}\)
= l =  \( \dfrac{λ}{2}\)

Or,   λ = 2 x 2 = 4m

Thus, sound travels through steel at a speed of v = νλ
v = 4 x 2.53 x 103

=10.12 km/s

Answered by Abhisek | 1 year ago

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