Wave Motion 1 Question 16

16. A harmonically moving transverse wave on a string has a maximum particle velocity and acceleration of 3m/s and 90m/s2 respectively. Velocity of the wave is 20m/s. Find the waveform.

(2005, 2M)

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Answer:

Correct Answer: 16. y=(0.1 m)sin[(30rad/s)t±(1.5 m1)x+ϕ]

Solution:

  1. Maximum particle velocity,

ωA=3m/s(i)

Maximum particle acceleration,

ω2A=90m/s2(ii)

Velocity of wave, ωk=20m/s(iii)

From Eqs. (i), (ii) and (iii), we get

ω=30rad/sA=0.1m and k=1.5m1

Equation of waveform should be

y=Asin(ωt+kx+ϕ)y=(0.1m)sin[(30rad/s)t±(1.5m1)x+ϕ]



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