Question

A uniform rope of length l and mass m hangs vertically from a rigid support. A block of mass m is attached to the free end of the rope. A transverse pulse of wavelength $\lambda$ is produced at the lower end of the rope.The wavelength of the pulse, when it reaches the top of the rope is a$\lambda$.Find $a^2$

Answer 1

$Length=lmass=mwavelength=\lambda {\lambda }_1\alpha velocity\left(v_1\right)=\sqrt{\frac{T_1}{\mu }}Similarly,{\lambda }_2\alpha v_2=\sqrt{\frac{T_2}{\mu }}\frac{{\lambda }_2}{{\lambda }_1}=\sqrt{\frac{T_2}{T_1}}=\sqrt{\frac{(m_1+m_2)g}{m_{2}g}}=\sqrt{\frac{m_1+m_2}{m_2}}$