JEE Mains · Physics · STD 11 - Waves and sound
- JEE Mains 2020
- Medium
- Numerical
A uniform thin rope of length \(12\, m\) and mass \(6\, kg\) hangs vertically from a rigid support and a block of mass \(2\, kg\) is attached to its free end. A transverse short wavetrain of wavelength \(6\, cm\) is produced at the lower end of the rope. What is the wavelength of the wavetrain (in \(cm\) ) when it reaches the top of the rope \(?\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(12\)
Step-by-step Solution
Detailed explanation
\(V \propto \lambda \quad T _{2}=8 g\)
\(T _{1}=2 g\)
\(\frac{ V _{1}}{ V _{2}}=\frac{\lambda_{1}}{\lambda_{2}}\)
\(\lambda_{2}=\frac{ V _{2}}{ V _{1}} \lambda_{1}=\sqrt{\frac{ T _{2}}{ T _{1}}} \times \lambda_{1}\)
\(=\sqrt{\frac{8 g }{2 g }} \lambda_{1}=2 \times 6=12 cm\)
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