The graph shows a wave at t -0 travelling to the right with a velocity of 4 m - s- The equation that best represents the wave isA- yx- t-2 sin- x-4- t metresB- yx- t-2 sin 16 - x-8 - t metres- yx- t-4 sin- x-4- t metresD- yx- t-2 sin- x-4- metres

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Wave Equation

The graph sho...

Question

The graph shows a wave at t = 0 travelling to the right with a velocity of 4 m/s. The equation that best represents the wave is

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Solution

The correct option is A
Let equation of the wave is
$y = A s i n (ω t - k x + ϕ_{0})$
The particle at origin is moving downwards (from graph) at $t = 0, s o ϕ_{0} = π .$ Also A = 2 m from graph.
From graph, $λ = 8 m, s o k = \frac{2 π}{λ} = \frac{π}{4}$
$ω = v k = \frac{4 \times π}{4} = π$
Putting all the values
$y = 2 s i n [π t - \frac{π}{4} x + π] \Rightarrow y = 2 s i n [\frac{π}{4} x - π t]$

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The graph shows a wave at t = 0 travelling to the right with a velocity of 4 m/s. The equation that best represents the wave is

The correct option is A Let equation of the wave is y=Asin(ωt−kx+ϕ0) The particle at origin is moving downwards (from graph) at t=0, so ϕ0=π. Also A = 2 m from graph. From graph,λ=8m,so k=2πλ=π4 ω=vk=4×π4=π Putting all the values y=2 sin[πt−π4x+π]⇒y=2 sin[π4x−πt]