Question

Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:

a) the magnitude of its acceleration is a maximum

b) the magnitude of its displacement is a maximum

c) the magnitude of its displacement is a minimum

d) the magnitude of its displacement is half the amplitude

e) the magnitude of its displacement is one fourth the amplitude

Answer 1

When the string carrying a sinusoidal wave the displacement of any point on it is given by y = A sin Wt because it executes simple harmonic motion the velocity V = dy/dt = AW cos Wt the acceleration a = dy/dt = AW cos Wt the acceleration a = dV/dt = -AW^2 Sin Wt = -AW^2 Cos(Wt - 90) => a = -w^2 y From the above expressions we can see that * the speed and displacement are in out of phase i.e when one is maximum the other one is minimum => when the speed is maximum, the displacement is minimum * the speed and acceleration are also in out of phase => the speed is maximum when the magnitude of acceleration is minimum so correct options card is 'C'