A transverse harmonic disturbance is produced in a

Question

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.

Jitender Pal · Accepted Answer

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 )

A_max = a ω² = 90 m/s² . . . . . . . . . . . . . . . . . . . (ii)

Velocity of wave v = 20 m/s . . . . . . . . . . . . . . . . (iii)

Dividing (ii) by (i)

Aω²/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
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