Statement-1: For a transverse wave described by $y (x, t) = A sin (k x - ω t)$ , the maximum particle speed is $A ω$ .
Statement-2: The wave speed (phase speed) for the wave described in Statement-1 is $ω / k$ .

Question

Statement-1: For a transverse wave described by $y (x, t) = A sin (k x - ω t)$ , the maximum particle speed is $A ω$ .

Statement-2: The wave speed (phase speed) for the wave described in Statement-1 is $ω / k$ .

TestHub · Accepted Answer

For a wave y ( x , t ) = A sin ( k x − ω t ) , the particle velocity is v p ​ = ∂ t ∂ y ​ = − A ω cos ( k x − ω t ) . The maximum particle speed is ∣ v p ​ ∣ max ​ = A ω , so Statement-1 is true. The wave speed (phase speed) is v = k ω ​ , so Statement-2 is also true. However, Statement-2 does not explain Statement-1, as they describe different aspects of the wave.

Physics - Wave on String Question with Solution | TestHub

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