First slide

Travelling wave

Question

Fig. below shows the wave $y = Asin (ωt - kx)$ at any instant travelling in the +ve x-direction. What is the slope of the curve at B

Moderate

A

$ω / A$
B

$k / A$
C

$kA$
D

$ωA$

Solution

The particle velocity is maximum at B and is given by $\frac{dy}{dt} = {(v_{p})}_{\max} = ωA$
Also wave velocity is $\frac{dx}{dt} = v = \frac{ω}{k}$
So slope $\frac{dy}{dx} = \frac{{(v_{p})}_{\max}}{v} = kA$

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