A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?
The disturbance takes 0.5 s to reach the other end of the string.
Explanation
This question tests the concept of speed of transverse waves on a stretched string. From the textbook context, the speed of a transverse wave depends on the tension (restoring force) and the linear mass density (inertial property). The formula v = is used, where T is tension and μ is linear mass density. The time is then calculated using the relation time = distance/speed.
Solution Steps
Step 1: Calculate the linear mass density (μ) of the string. μ = mass/length = 2.50 kg / 20.0 m = 0.125 kg m⁻¹
Step 2: Calculate the speed of the transverse wave using the formula. v = = = = 40 m s⁻¹
Step 3: Calculate the time taken for the disturbance to travel the length of the string. Time = Distance / Speed = 20.0 m / 40 m s⁻¹ = 0.5 s