Sound WavesHard
Question
A transverse wave is represented by y = Asin(ωt - kx) . For what value of the wavelength is the wave velocity equal to the maximum particle velocity ?
Options
A.πA/2
B.πA
C.2πA
D.A
Solution
The given wave equation is
y = Asin(ωt - kx)
Wave velocity, v =
.....(i)
Particle velocity, vp =
= Aω cos(ωt - kx)
Maximum particle velocity, (vP)max = Aω
According to the given quation
v = (vP)max
= Aω [Using (i) and (ii)]
or
λ = 2πA
y = Asin(ωt - kx)
Wave velocity, v =
.....(i)Particle velocity, vp =
= Aω cos(ωt - kx)Maximum particle velocity, (vP)max = Aω
According to the given quation
v = (vP)max
= Aω [Using (i) and (ii)]or
λ = 2πA
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