A rod, 1 cm2 x 200 cm and mass 2 kg, is clamped at its center. When vibrating longitudinally it emits its third overtone in unison with a tuning fork making 6000 vps. How much will the rod be elongated if, when clamped at one end, a stretching force of 980 N is applied to the other end?
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Expert's answer
2020-07-14T08:51:41-0400
Explanations & Calculations
Velocity of the longitudinal waves through a dense medium = ρE
During the 3rd overtone the length of the rod (l )= 27λ when the rod is clamped at its center. therefore, the frequency of the third overtone
f=λv=2l7v=2l7ρE
ρ=volumem=200×10−6m32kg=10000kgm−3
Since the rod is in resonance with the tuning fork, f =6000
Therefore,
6000E=2×2m710000E=1.17551×1011Nm−2
Therefore, the elongation (e) could be calculated to be,
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