Question

A uniform rope of mass m length L hangs from the ceiling.$A$ small wave pulse is created at bottom, then which of following is correct regarding wave pulse.

• A. Rate of change of speed with respect to time varies.
• B. Rate of change of speed with respect to time is constant.
• C. Rate of change of speed with respect to time is zero
• D. Wave speed varies.

Answer 1

Answer: (B), (D)

The correct options are
B Rate of change of speed with respect to time is constant.
D Wave speed varies.

$T=m_{1}g$

$T=\left(\frac{m}{L}\right)xg$

Speed of wave$V=\sqrt{\frac{mg/L}{m/l}}=\sqrt{xg}$

Hence wave speed varies with $x$.

$a=\frac{dv}{dt}=\sqrt{g}\times \frac{1}{2\sqrt{x}}\frac{dx}{dt}=\frac{\sqrt{g}}{2\sqrt{x}}V=g/2$

Rate of change of speed with respect to time$=\frac{d}{dt}\left(V\right)=g/2=$constant