JEE Main 2023 · 24 January · morning · Single correct · +4 / −1
A travelling wave is described by the equation
y(x,t) = [0.05 sin (8x - 4t)] m
The velocity of the wave is : [all the quantities are in SI unit]
- (a) 4 ms⁻¹
- (b) 2 ms⁻¹
- (c) 8 ms⁻¹
- (d) 0.5 ms⁻¹
Answer and solution
Answer (d) 0.5 ms⁻¹
Solution
Physics sir · 3 steps
Read ω and k straight off the sine, then the wave speed is just their ratio.
- Match the form. A travelling wave has the form y = A sin(kx - ω t). Comparing with 0.05 sin(8x - 4t) gives k = 8 rad m⁻¹ and ω = 4 rad s⁻¹.
v = ω/k = 4/8
- Direction check. The minus sign between kx and ω t means the wave moves along +x. It does not change the speed.
- So. v = 0.5 m s⁻¹, which is option (d).
The idea to keep. For any wave sin(kx ± ω t), the speed is the coefficient of t divided by the coefficient of x. Do not swap them.
Answer from the NTA final answer key. Solution by PrepWiser.