The displacement of a particle of a string carrying a travelling wave is given by y=3sin[6.28(0.50x−50t)] (x→in cm,y→cm,t→in second). What would be the speed of the wave?
A
200cm s−1
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B
150cm s−1
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C
100cm s−1
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D
50cm s−1
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Solution
The correct option is C100cm s−1 Displacement of a particle on string(carrying a travelling wave) is given, y=3sin[6.28(0.5x−50t)] where x,y are in cm, t is in seconds. Comparing with equation of progressive wave, y=Asin(kx−ωt) We get k=6.28×0.5;ω=6.28×50 We know that k=2πλ ⇒2×3.14λ=6.28×0.5 ⇒λ=2cm and ω=2πf ⇒2πf=6.28×50 ⇒6.28f=6.28×50 ⇒f=50Hz Speed of wave is, v=fλ ∴v=50×2=100cm s−1