Q.

For the wave shown in figure, write the equation of this wave if its position is shown at t = 0 Speed of wave is v = 300 m/s.

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a

y=(0.06m)cos⁡78.5m−1x+23562s−1tm

b

y=(0.06m)sin⁡78.5m−1x−23562s−1tm

c

y=(0.06m)sin⁡78.5m−1x+23562s−1tm

d

y=(0.06m)cos⁡78.5m−1x−28562s−1tm

answer is B.

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Detailed Solution

The amplitude, A=0.06m    52λ=0.2m ∴ λ=0.08m     f=vλ=3000.08=3750Hz     k=2πλ=78.5m−1 and ω=2πf=23562rad/sAt  t=0,x=0, dydx= positive and the given curve is a sine curve. Hence, equation of wave travelling in positive x-direction should have the form, y(x,t)=Asin⁡(kx−ωt) Substituting the values, we have y=(0.06m)sin⁡78.5m−1x−23562s−1tm
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For the wave shown in figure, write the equation of this wave if its position is shown at t = 0 Speed of wave is v = 300 m/s.