Wave motionMediumBloom L3
Question
A sinusoidal wave travelling in the positive direction of x on a stretched string has amplitude 2.0 cm, wavelength 1 m and wave velocity 5.0 m/s. At x = 0 and t =0, it is given that displacement y = 0 and $\frac{\partial y}{\partial t} < 0$. Express the wave function correctly in the form y = f(x, t) :-
Options
A.y = (0.02 m) sin 2π (x–5t)
B.y = (0.02 cm) cos 2π(x–5t)
C.y = (0.02 m) sin 2π$\left( x - 5t + \frac{1}{4} \right)$
D.y = (0.02 cm) cos 2π$\left( x - 5t + \frac{1}{4} \right)$
Solution
Sol. y = A sin(ωt – kx + φ)
Α = 2cm, λ = 1m, f = $\frac{v}{\lambda}$= 5 Hz
ω = 10π
At x = 0, t = 0, y = 0
sinφ = 0
$\frac{dy}{dt} < 0.$ φ = π
y = 0.02 sin (10πt – 2πx + π)
y = 0.02 sin(2πx – 10πt)
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