Question:
A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20 m. If a transverse jerk is struck at one end of the string, the time taken for the disturbance to reach the other end is:
A string of mass 2.5 kg is under a tension of 200 N. The length of the stretched string is 20 m. If a transverse jerk is struck at one end of the string, the time taken for the disturbance to reach the other end is:
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You can combine the two formulas into a single step to minimize calculation steps:
Plugging values directly into this consolidated form:
Updated On: Jun 10, 2026
- 0.5 s
- 1.0 s
- 0.25 s
- 2.0 s
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The Correct Option is A
Solution and Explanation
Concept:
When a sudden transverse displacement or jerk is applied to a taut string, it generates a transverse wave pulse that propagates along the length of the string. The linear propagation speed (v) of a transverse wave in a stretched string depends entirely on two mechanical properties of the medium:
• The tension (T) maintained within the string.
• The mass per unit length or linear mass density () of the string material.
The standard wave velocity equation derived from Newton's Second Law is: Once the wave speed is determined, the time (t) required for the wave pulse to travel a specified distance (L) along the string can be calculated using basic kinematics:
Step 1: Calculating the Linear Mass Density ()
The problem provides the following parameters:
• Total mass of the string, M = 2.5 kg
• Stretched length of the string, L = 20 m
• Tension inside the string, T = 200 N
Linear mass density () is the mass of the string divided by its total length:
Step 2: Calculating Wave Velocity (v)
Substitute the values of tension T = 200 N and linear mass density = 0.125 kg^-1 into the velocity formula: To simplify the fraction under the radical, rewrite 0.125 as a fraction (18): The transverse wave pulse travels along the string at a constant velocity of 40 ms^-1.
Step 3: Calculating Travelling Time (t)
The disturbance needs to travel the entire length of the string, which is L = 20 m. Using the kinematic relation: Thus, the time taken for the disturbance to reach the opposite end of the string is exactly 0.5 s.
• The tension (T) maintained within the string.
• The mass per unit length or linear mass density () of the string material.
The standard wave velocity equation derived from Newton's Second Law is: Once the wave speed is determined, the time (t) required for the wave pulse to travel a specified distance (L) along the string can be calculated using basic kinematics:
Step 1: Calculating the Linear Mass Density ()
The problem provides the following parameters:
• Total mass of the string, M = 2.5 kg
• Stretched length of the string, L = 20 m
• Tension inside the string, T = 200 N
Linear mass density () is the mass of the string divided by its total length:
Step 2: Calculating Wave Velocity (v)
Substitute the values of tension T = 200 N and linear mass density = 0.125 kg^-1 into the velocity formula: To simplify the fraction under the radical, rewrite 0.125 as a fraction (18): The transverse wave pulse travels along the string at a constant velocity of 40 ms^-1.
Step 3: Calculating Travelling Time (t)
The disturbance needs to travel the entire length of the string, which is L = 20 m. Using the kinematic relation: Thus, the time taken for the disturbance to reach the opposite end of the string is exactly 0.5 s.
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