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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 \lambda1 is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \lambda2. The ratio \lambda2/\lambda1 is:

  • Option 1)

    \sqrt{\frac{\text{m}_{1}}{\text{m}_{2}}}

  • Option 2)

    \sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{2}}}

  • Option 3)

    \sqrt{\frac{\text{m}_{2}}{\text{m}_{1}}}

  • Option 4)

    \sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{1}}}

 

Answers (1)

best_answer

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 = ( m1 + m2 ) 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)

\sqrt{\frac{\text{m}_{1}}{\text{m}_{2}}}

This option is incorrect

Option 2)

\sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{2}}}

This option is correct

Option 3)

\sqrt{\frac{\text{m}_{2}}{\text{m}_{1}}}

This option is incorrect

Option 4)

\sqrt{\frac{\text{m}_{1}+\text{m}_{2}}{\text{m}_{1}}}

This option is incorrect

Posted by

Aadil

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