# A uniform rope of length L and mass m1 hangs vertically from a rigid support. A block of mass m2 is attached to the free end of the rope. A transverse pulse of wavelength 1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is 2. The ratio 2/1 is: Option 1) Option 2) Option 3) Option 4)

As we discussed in

Speed of wave on string -

$v= \sqrt{\frac{T}{\mu }}$

- wherein

$T=$ Tension in the string

$\mu =$ linear mass density

T1 = m2g

T2 = ( m+ m) g

$V \alpha \sqrt{T}$

$\lambda\: \alpha \sqrt{T}$

$\therefore \frac{\lambda _{1}}{\lambda _{2}}=\frac{\sqrt{T_{1}}}{\sqrt{T_{2}}} \Rightarrow \frac{\lambda _{1}}{\lambda _{2}}= \frac{\sqrt{m_{1}+ m_{2}}}{\sqrt{m_{2}}}$

$\sqrt{\frac{m_{1}+m_{2}}{m_{2}}}$

Option 1)

This option is incorrect

Option 2)

This option is correct

Option 3)

This option is incorrect

Option 4)

This option is incorrect

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