A steel rod 100 cm long is clamped at its mid-point. the fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?

5.06 km/s

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6.06 km/s

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7.06 km/s

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8.06 km/s

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Solution

The correct option is A 5.06 km/s
As steel rod of length $l = 100 c m = 1 m$ is clamped at its mid-point, the mid-point will behave as node and the end points as antinodes i.e,
$l = \frac{λ}{2}$
or $λ = 2 l = 2 m$
Moreover, frequency $ν = 2.53 k H z$
Hence speed of sound $v = ν λ = 2.53 k H z \times 2 m$ $= 5.06 k m / s$

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A steel rod 100 cm long is clamped at its mid-point. the fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?

The correct option is A 5.06 km/sAs steel rod of length l=100cm=1m is clamped at its mid-point, the mid-point will behave as node and the end points as antinodes i.e,l=λ2 or λ=2l=2mMoreover, frequency ν=2.53kHzHence speed of sound v=νλ=2.53kHz×2m =5.06km/s