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Question : 16 of 27
Marks: +1, -0
A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be 2.53 kHz. What is speed of sound in steel?
Solution:  
A rod clamped in the middle has antinodes (A) at its ends and node (N) at the point of clamping. In fundamental mode, thus the length of the rod is
Where l=l = length of rod
and also l=l = wavelength of the wave
Here, l=100l = 100 cm
υ=2.53 kHz=2.53×103 Hz\upsilon = 2.53 \text{ kHz} = 2.53 \times 10^3 \text{ Hz}
∴ λ=2×100=200 cm\lambda = 2 \times 100 = 200 \text{ cm}
If vv be the speed of sound in steel, then
v=υλ=2.53×103×200v = \upsilon \lambda = 2.53 \times 10^3 \times 200
=506×103 cm s−1= 506 \times 10^3 \text{ cm s}^{-1}
=5.06×103 ms−1= 5.06 \times 103 \text{ ms}^{-1}
v=5.06 km s−1.v = 5.06 \text{ km s}^{-1}.
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