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Waves

Question

A 4 kg block is suspended from the ceiling of an elevator through a spring having a linear mass density of 19.2 x 10^-3 kg m^-3 . Find the speed with respect to spring with which a wave pulse can proceed on the spring if the elevator accelerates up at the rate of 2.0 ms^-2.
Take g = 10 ms^-2

30 m/s

42 m/s

46 m/s

50 m/s

Solution

50 m/s

Given:-

m = 19.2 x 10^-3 kg /m

Now see the free body diagram

The equation for the motion

T - 4g - 4a = 0

⇒ T = 4 ( a + g )

= 4 ( 2 + 10)

T = 48 N

Now wave speed

v = $\sqrt{(\frac{T}{m})}$

= $\sqrt{2.5 \times 10^{- 3}}$

v = 50 m/s