Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String
Two strings A and B , constructed from the identical material, are subjected to the same tension. The radius of string A is twice the radius of string B . A transverse wave propagates on A with speed v_A and on B with speed v_B . What is the ratio v_A/v_B ?
Options
- A1 4
- B1 2
- C2
- D4
Correct answer
B. 1 2
Step-by-step solution
The speed of a transverse wave on a string is given by v = T , where T is the tension and is the linear mass density. The linear mass density can be written as = r^2 , where is the density of the material and r is the radius of the string. Since both strings are made of the same material and subjected to the same tension, T and are constant. Therefore, the speed v is inversely proportional to the radius r : v 1 r The ratio of the speeds is: v_A v_B = r_B r_A Given that r_A = 2r_B , substituting this value gives: v_