Question
Download Solution PDFA wave travelling along the x-axis is described by the equation y = 0.005 cos (αx - βt). If the wavelength and the time period of the wave are 0.08 m and 2 seconds respectively. Find the values of α and β.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The general equation of wave motion is given by:
y = Asin (kx - ωt)
where A = amplitude, ω = angular frequency, k = angular wavenumber, t = time, and x is position
- Wavelength (λ): Distance between two nearest particles vibrating in the same phase.
- Frequency (f): Number of vibrations complete by a particle in one second.
- Time Period (T): Time taken by the wave to travel a distance equal to one wavelength.
- Amplitude (A): Maximum displacement of vibrating particles from the mean position.
The relationship between frequency (f), wavelength (λ), and velocity (v) of a wave is given by:
f × λ = v
CALCULATION:
Given that:
y = 0.005 cos (αx - βt)
λ = 0.08 m, and Time period (T) = 2 sec
By comparing the given equation with the general equation we get:
α = k and β = ω
We know that ω = 2π/T and k = 2π/λ
α = 2π/λ
β = 2π/T
α = 2π/0.08
α = 25π
β = 2π/2
β = π
Hence option 1 is correct
Last updated on Jul 4, 2025
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