Question

Consider a rope fixed at both ends under tension so that it is horizontal (i.e. assume the rope is along x-axis, with gravity acting along z-axis). Now the right end is continually oscillated at high frequency $n$ (say $n = 100 \, \text{Hz}$) horizontally and in a direction along the rope; amplitude of oscillation is negligible. The oscillation travels along the rope and is reflected at the left end.

• A. BLANK-1: travelling, oscillating, stationary, regular
• B. BLANK-2: transverse, longitudinal, regular, irregular
• C. BLANK-3: transverse, longitudinal, regular, irregular
• D. BLANK-4: equal to, half, double, independent from

Hint:

In a tensioned rope, waves propagate with velocity determined by the tension and mass per unit length. For a given wave, the frequency remains unchanged by reflection.

Answer 1

The Correct Option is A

After the initial phase, the rope exhibits travelling transverse waves, which are a result of the superposition of the left and right traveling waves. The frequency of the resulting wave is equal to the frequency of the oscillating source. The dimensional analysis of wave velocity in such a system leads to the result $\sqrt{\frac{g}{l}}$.