A wave travelling along the x−axis is described by the equation y(x,t)=0.008cos(αx−βt). If the wavelength and time period of the wave are 0.16m and 6.0 respectively, then α and β in appropriate units are
A
α=25.00π,β=π
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B
α=12.50π,β=π2
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C
α=12.50π,β=π3
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D
α=0.08π,β=2π
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Solution
The correct option is Cα=12.50π,β=π3 Given, y(x,t)=0.008cos(αx−βt)....(1) Wavelength (λ)=0.16m Time period (T)=6.0s Comparing Eq.(1) with standard equation of a travelling wave, y=Asin(kx−ωt+ϕ) We get, A=0.008m,k=αm−1,ω=βs−1 we know that wave number is, k=2πλ and angular frequency, ω=2πT ⇒α=2πλ ⇒α=2π0.16=12.5πunits Similarly β=2πT ⇒β=2π6=π3units