A thick uniform rope of Length L is hanging from a rigid support

Question

A thick uniform rope of Length L is hanging from a rigid support. A transverse wave of wavelength $λ_{0}$ is set up in the middle of the rope. The wavelength of the wave as it reaches the top most point is

Smart Achievers · Accepted Answer

(2)

$Here frequency f is constant. Speed of wave$

$v = \sqrt{\frac{T}{μ}}$

$\Rightarrow \frac{v_{1}}{v_{2}} = \frac{λ_{1}}{λ_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{M g / 2}{M g}}$

$\Rightarrow λ_{2} = \sqrt{2} λ_{1} = \sqrt{2} λ_{0}$

Solution

Q.
A thick uniform rope of Length L is hanging from a rigid support. A transverse wave of wavelength $λ_{0}$ is set up in the middle of the rope. The wavelength of the wave as it reaches the top most point is

1 $2 λ_{0}$

2 $\sqrt{2} λ_{0}$

3 $\frac{λ_{0}}{\sqrt{2}}$

4 $λ_{0}$

Ans.
(2)

$Here frequency f is constant. Speed of wave$

$v = \sqrt{\frac{T}{μ}}$

$\Rightarrow \frac{v_{1}}{v_{2}} = \frac{λ_{1}}{λ_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{M g / 2}{M g}}$

$\Rightarrow λ_{2} = \sqrt{2} λ_{1} = \sqrt{2} λ_{0}$

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Solution

Q. A thick uniform rope of Length L is hanging from a rigid support. A transverse wave of wavelength λ0 is set up in the middle of the rope. The wavelength of the wave as it reaches the top most point is

1 2λ0

2 2λ0

3 λ02

4 λ0

Ans. (2) Here frequency f is constant. Speed of wave v=Tμ ⇒v1v2=λ1λ2=T1T2=Mg/2Mg ⇒λ2=2λ1=2λ0