Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
A wave travelling on a string has the equation y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . In which direction does the wave travel?
Options
- ANegative x -direction
- BPositive x -direction
- CPositive y -direction
- DNegative y -direction
Correct answer
A. Negative x -direction
Step-by-step solution
The given equation of the wave is y = (0.10 mm ) [(31.4 m ⁻¹)x + (314 s ⁻¹)t] . Comparing this with the standard wave equation y = A (kx + t) , we observe that the argument of the sine function has a positive sign between the spatial and temporal terms. For a point of constant phase, kx + t = constant . Differentiating with respect to time t , we get k dx dt + = 0 , which gives the wave velocity v = dx dt = - k . Since the velocity is negative, the wave travels in the negative x -direction.