Question
Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of the waves in A and B is
BITSAT
Physics
Waves and Sound
2022
BITSAT 2022
BITSAT Physics Question (2022) — Solution
Options
- A. 1: 2
- B. 1: 2
- C. 1: 2 2
- D. 3: 2 2
Answer
C. 1: 2 2
Step-by-step solution
The velocity of transverse waves is given by v= T m where, T= Tension and m= mass per unit length of the wire. If r is the radius of the wire and its density then, m= r^2 v= T m = T r^2 v_A= T_A r_A and v_B= T_B r_B Now, v_A v_B = T_A T_B r_B r_A r_A=2 r_B and T_A= 1 2 T_B Hence, v_A v_B = 1 2 2
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