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Question

Write the equation of the wave shown in figure, if its position is shown at t=0.6 sec. The wavelength is 15 cm and amplitude is 4 cm and the crest X was at x=0 at t=0.



A
y(x,t)=(2 cm)sin[(1.68 rad/s)t(1 cm1)x]
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B
y(x,t)=sin[(3.2 rad/s)t(0.42 cm1)x]
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C
y(x,t)=(2 cm)cos[(3.2 rad/s)t(0.42 cm1)x]
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D
y(x,t)=(4 cm)cos[(1.68 rad/s)t(0.42 cm1)x]
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Solution

The correct option is D y(x,t)=(4 cm)cos[(1.68 rad/s)t(0.42 cm1)x]
Given that, amplitude (A)=4 cm and wavelength λ=15 cm
K=2πλ=2π15=0.42 cm1
The wave travelled a distance 2.4 m in 0.6 sec. Hence speed of the wave
v=2.40.6=4 cm/s
angular frequency (ω)=v×K
=4×0.42=1.68 rad/s.
Since the wave is travelling along positive x-direction and crest X was at x=0 at t=0, so we can write the wave equation as
y(x,t)=Acos(Kxωt)
or y(x,t)=Acos(ωtKx)
[as cos(θ)=cosθ]
Therefore , the desired equation is
y(x,t)=(4 cm)cos[(1.68 rad/s)t(0.42 cm1)x]

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