Question

A thick uniform rope of length L is hanging from a rigid support. A transverse wave of wavelength ${\lambda }_0$ is set up at the middle of rope as shown figure. The wavelength of the wave as it reaches to the topmost point is

• A. $2{\lambda }_0$
• B. $\sqrt{2}{\lambda }_0$
• C. $\frac{{\lambda }_0}{\sqrt{2}}$
• D. ${\lambda }_0$

Answer 1

The correct option is B $\sqrt{2}{\lambda }_0$

Speed of pulse at distance $x$ from bottom $v=\sqrt{gx}$
while travelling from mid point to the top, frequency remains unchanged
$\frac{v_1}{{\lambda }_1}=\frac{v_2}{{\lambda }_2}\Rightarrow \frac{\sqrt{g\left(L/2\right)}}{{\lambda }_0}=\frac{\sqrt{gL}}{{\lambda }_2}={\lambda }_2=\sqrt{2}{\lambda }_0$