MHT CET Medical202624 April 2026Evening ShiftPhysicsWaves and SoundActual
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
Options
- Am₁ + m₂ m₂
- Bm₂ m₁
- Cm₁ + m₂ m₁
- Dm₁ m₂
Correct answer
A. m₁ + m₂ m₂
Step-by-step solution
The velocity of a transverse wave on a string is given by v = T , where T is the tension and is the mass per unit length. Since the frequency f of the wave remains constant as it travels up the rope, the wavelength is proportional to the wave velocity v . Thus, T . At the lower end of the rope, the tension is due to the attached block of mass m₂ . T₁ = m₂ g At the upper end of the rope, the tension is due to the mass of the rope and the attached block. T₂ = (m₁ + m₂) g The ratio of the wavelengths is given by: ₂ ₁