For the wave shown in figure- write the equation of this wave if its position is shown at t-0 - Speed of wave is v-30 m - sx m A- -y-0-06 m cos-78-5 m -1 x-23562 s -1 t- mB- y-0-06 m sin-78-5 m -1 x-23562 s -1 t- mC- y-0-06 m cos-78-5 m -1 x-28562 s -1 t- mD- y-0-06 m sin-78-5 m -1 x-23562 s -1 t- m

The correct option is D The amplitude, A = 0.06 m 5/2λ = 0.2 m ∴λ = 0.08 m f = v/λ = 30/0.080 = 375 Hz k = 2 π/λ = 78.5 m^ 1 and ω = 2 π f = 2356.2 rad/s ...

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Byju's Answer

Standard XII

Physics

Wave Equation

For the wave ...

Question

For the wave shown in figure, write the equation of this wave if its position is shown at t = 0. Speed of wave is v = 30 m/s.

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Solution

The correct option is B
The amplitude, A = 0.06 m
$\frac{5}{2} λ = 0.2 m ∴ λ = 0.08 m f = \frac{v}{λ} = \frac{30}{0.080} = 375 H z k = \frac{2 π}{λ} = 78.5 m^{- 1} a n d ω = 2 π f = 2356.2 r a d / s A t t = 0, x = 0, \frac{d y}{d x} = p o s i t i v e$
And the given curves is a since curve.
Hence, equation of wave travelling in positive x – direction should have the form,
$y (x, t) = A s i n (k x - ω t)$
Substituting the values, we have
$y = (0.06 m) s i n [(78.5 m^{- 1}) x - (2356.2 s^{- 1}) t] m$

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