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A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is 3 m/s and maximum transverse acceleration is 90 m/s 2 . If the wave velocity is 20 m/s then find the waveform.

A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is 3 m/s and maximum transverse acceleration is 90 m/s2. If the wave velocity is 20 m/s then find the waveform.    

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
7 years ago
Hello Student,
Please find the answer to your question
KEY CONCEPT : The wave form of a transverse harmonic disturbance is
y = a sin (ω t ± k x ± ϕ)
Given v max = a ω = 3 m/s . . . . . . . . . . . . . . . . ( i )
Amax = a ω2 = 90 m/s2 . . . . . . . . . . . . . . . . . . . (ii)
Velocity of wave v = 20 m/s . . . . . . . . . . . . . . . . (iii)
Dividing (ii) by (i)
2/a ω = 90/3 ⇒ ω = 30 rad/s . . . . . . . . . . . . . . .(iv)
Substituting the value of ω in (i), we get
a = 3/30 = 0.1 m . . . . . . . . . . . . . . . . . (v)
Now, k = 2π /ℷ = 2π / v/v = ω/v = 30/20 = 3/2 . . . . . . . . . . . . . . . . (vi)
From (iv), (v) and (vi) the wave form is
y = 0.1 sin [30 t ± 3/2 x ± ϕ]

Thanks
Jitender Pal
askIITians Faculty

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