First slide

Speed of wave

Question

A wave equation which gives the displacement along the direction Y is given by the equation $y = 10^{4} \sin (60 t + 2 x)$ , where x and y are in metres and t is time in seconds. This represents a wave

Moderate

A

Travelling with a velocity of 30 m/sec in the negative X direction
B

Of wavelength 2 $π$ metre
C

Of frequercy $\frac{60}{π}$ Hz
D

Of amplitude $10^{4}$ metre travelling along the positive X direction

Solution

On comparing the given equation with $y = a \sin (ωt + kx)$ , it is clear that wave is travelling in negative x-direction. Its amplitude $a = 10^{4}$ m and $ω = 60, k = 2 .$ . Hence frequency $n = \frac{ω}{2 π} = \frac{60}{2 π} = \frac{30}{π} Hz$
$k = \frac{2 π}{λ} = 2 \Rightarrow λ = π m and v = \frac{ω}{k} = \frac{60}{2} = 30 m / s$

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