Question

A uniform rope of length 10 cm and mass 15 kg hangs vertically from a rigid support. A block of mass 5kg is attached to the free end of the rope. A transverse pulse of wavelength 0.08 m is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope will be:

• A. 0.08 m
• B. 0.04 m
• C. 0.16 m
• D. 0 m

Answer 1

Answer: (C)

Velocity at lower end,
$V_1=\sqrt{\frac{50\times 10\times 10^{-2}}{15}}$
${\lambda }_1=0.08m$
$f_1=\frac{V_1}{{\lambda }_7}$
Velocity at upper and
$=V_2=\sqrt{\frac{200\times 10\times 10^{-2}}{15}}$
$f_2=\frac{V_2}{{\lambda }_2};f_1=f_2$
$\sqrt{\frac{50\times 10\times 10^{-2}}{15}}$ ;
${\lambda }_2=\sqrt{\frac{200\times 10\times 10^{-2}}{15}}\times 0.08$
$\sqrt{50}\times {\lambda }_2=\sqrt{200}\times 0.08$
${\lambda }_2=2\times 0.08$
${\lambda }_2=0.16m$