Certain wave travels with a velocery of V=AN/ Where A IS a constant Calculate Its Group velocity
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A wave travelling along a string is described by,
y(x,t)=0.005sin(80.0x−3.0t), in which the numerical constants are in SI units (0.005 m, 80.0 rad m
−1
and 3.0 rad s
−1
). Calculate :
(a) the amplitude
(b) the wavelength
(c) the period and frequency of the wave.
Also, calculate the displacement y of the wave at a distance x = 30.0 cm and time t = 20 s?
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Answer
We know that
general equation of wave
y(x,t)=Asin(kx−ωt)
comparing this equation with given equation
1) A=0.005m → amplitude
k=80
ω=3
2) λ=
k
2π
=
80
2π
=(
40
π
)m
3) Time period T=
ω
2π
=
3
2π
sec
frequency f=
T
1
=
2π
3
Hz
4) Displacement at x=0.3m
t=20 sec
y=0.005sin(80×0.3−3×20)
=0.005sin(24−60)=0.005sin(−36)
=0.00495m
y=4.9mm.
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