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Question

A wave travelling along the xaxis is described by the equation y(x,t)=0.008cos(αxβt). If the wavelength and time period of the wave are 0.16 m 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 C α=12.50π, β=π3
Given,
y(x,t)=0.008cos(αxβt) ....(1)
Wavelength (λ)=0.16 m
Time period (T)=6.0 s
Comparing Eq.(1) with standard equation of a travelling wave,
y=Asin(kxωt+ϕ)
We get,
A=0.008 m, k=α m1, ω=β s1
we know that wave number is, k=2πλ and angular frequency, ω=2πT
α=2πλ
α=2π0.16=12.5π units
Similarly
β=2πT
β=2π6=π3 units

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