Question

A sinusoidal wave is generated by moving the end of a string up and down, periodically. The generator must apply the energy at maximum rate when the end of the string attached to generator has ……….X and least power when the end of the string attached to generator has ……….Y. The most suitable option which correctly fills blanks X and Y, is

• A. maximum displacement, least acceleration
• B. maximum displacement, maximum acceleration
• C. least displacement, maximum acceleration
• D. least displacement, least acceleration

Answer 1

The correct option is C least displacement, maximum acceleration

Power for a travelling wave on a string is given by
$P=pv{A}^2{\omega }^{2}co{s}^2(kx-\omega t)$
For the displacement wave,
$y=Asin(kx-\omega t)$
Power delivered is maximum when $co{s}^2(kx-\omega t)$ is maximum, which would be the case when sin $(kx-\omega t)$ is the least, i.e., displacement is minimum (acceleration is minimum). Power delivered is minimum when $co{s}^2(kx-\omega t)$ is minimum, which would be when $sin(kx-\omega t)$ is maximum, i.e., displacement is maximum (acceleration is maximum).