Question

A wave travelling along the x-axis is described by the equation y(x, t) = 0.005cos(αx-βt) . if the wavelength and the time period of wave are 0.08m and 2.0 s respectively , then α and β in appropriate units are [AIEEE 2008]​

Answer 1

Explanation :- As general equation is y (x,t) = acos(kx-ωt)

where, k = 2π/λ and ω = 2π/T

∴ y(x,t) = 0.005cos(αx -βt)

⟹2π/λ =α ⟹ 2π /T = β

So, α = 2π/0.08 = 25πm ⁻¹

So, α = 2π/0.08 = 25πm ⁻¹ and, β = 2π/2 = π s⁻¹

Answer 2

Given : λ=0.08 m T=2.0 s

The given equation is: y(x,t)=0.005cos(αx−βt)

On comparing with standard equation: y(x,t)=Acos(kx−wt)

∴ α=k= 2π/λ

⟹ α= 2π/0.08 =25π

Also, β=w= 2π/T

⟹ β= 2π/2

=π

HOPING THIS WILL HELP YOU PLZ MARK AS BRAINLIEST AND FOLLOW ME