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Question
How are the wave velocity V, frequency f and wavelength λ of a wave related? Derive the relationship.
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Solution
Let the velocity of a wave be V, time period T, frequency ν and wavelength λ. By the definition of wavelength,
Wavelength = Distance travelled by the wave in one time period i.e., in T second
Or, wavelength = Wave velocity × Time period
Or, λ = V × T
Or, λ = V × 1/ ν ...[As, T = 1/]
Therefore, V = ν λ
Therefore, Wave velocity = Frequency × wavelength
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