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 the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are :α = 25.00 π ; β = πα = , β = α = ; β = α = 12.50 π ; β =
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 the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are :α = 25.00 π ; β = πα = , β = α = ; β = α = 12.50 π ; β =
Solution
The given wave equation is y(x,t) = 0.005cos (αx – βt).
We know that the wave number k (which is equivalent to α) is given by 2π/λ, where λ is the wavelength.
Given that the wavelength λ = 0.08 m, we can substitute this into the equation to find α:
α = 2π/λ = 2π/0.08 = 25π rad/m.
The angular frequency ω (which is equivalent to β) is given by 2π/T, where T is the period.
Given that the period T = 2.0 s, we can substitute this into the equation to find β:
β = 2π/T = 2π/2.0 = π rad/s.
So, α = 25π rad/m and β = π rad/s.
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