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Question

# A sinusoidal wave travelling in the positive x-direction has an amplitude of 10 cm, wavelength 30 cm and frequency 6 Hz. The vertical displacement of the medium at t=0 and x=0 is also 10 cm.

A
Wave number is π15 cm1
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B
Time period of wave is 16 s
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C
Value of phase constant is π2
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D
Speed of wave is 1.8 m/s
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Solution

## The correct options are A Wave number is π15 cm−1 B Time period of wave is 16 s C Value of phase constant is π2 D Speed of wave is 1.8 m/sWave number (K)=2πλ=2π30=π15 rad/cm Time period (T)=1f=16 s Angular frequency w=2πf=2π×6=12π rad/s Speed of wave =f×λ=6×0.3=1.8 m/s Given that, amplitude A=10 cm and also y=10 cm at x=0 & t=0 Then, using y=Asin(ωt−kx+ϕ) 10=10sin(ϕ) or ϕ=π2 is the phase constant. Thus, options (a), (b), (c) and (d) are correct.

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