Question

A uniform rope of mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. The wavelength of the pulse, when it reaches the top is ______. (in m) 

विकल्प

• 0.06

• 0.12 

• 0.03

• 0.24

Answer 1

A uniform rope of mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. The wavelength of the pulse, when it reaches the top is 0.12. 

Explanation:

${\displaystyle \text{v}=\sqrt{\frac{\text{T}}{m}}=\text{f}\lambda }$

${\displaystyle \text{v} \alpha \lambda \sqrt{\text{T}}\Rightarrow {\text{T}}_1=2 \text{kg} {\text{T}}_2}$ = 6 + 2 =8 kg

${\displaystyle \frac{{\text{v}}_2}{{\text{v}}_1}=\frac{{\lambda }_2}{{\lambda }_1}=\sqrt{\frac{{\text{T}}_2}{{\text{T}}_1}}=\sqrt{\frac{8}{2}}=2}$

${\displaystyle {\lambda }_2=2{\lambda }_1=2\times 0.06}$ = 0.12 m