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 he disturbance take to reach the other end ?
Question
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 he disturbance take to reach the other end ?
Solution
To solve this problem, we need to use the formula for the speed of a wave on a stretched string, which is given by:
v = sqrt(T/μ)
where:
- v is the speed of the wave,
- T is the tension in the string, and
- μ is the linear mass density of the string.
First, we need to calculate the linear mass density of the string. This is given by the mass of the string divided by its length:
μ = m/L = 2.50 kg / 20.0 m = 0.125 kg/m
Next, we substitute the values for T and μ into the formula for v:
v = sqrt(200 N / 0.125 kg/m) = sqrt(1600 m²/s²) = 40 m/s
Finally, we find the time it takes for the disturbance to reach the other end of the string by dividing the length of the string by the speed of the wave:
t = L/v = 20.0 m / 40 m/s = 0.5 s
So, the disturbance takes 0.5 seconds to reach the other end of the string.
Similar Questions
A 0.220 kg string is attached to opposite sides of aroom that is 4.30 m across. If the string is pluckedand the resultant wave speed on the string is 18.0 m/s,what is the tension in the string?
Transverse waves with a speed of 46.5 m/s are to be produced on a stretched string. A 4.30-m length of string with a total mass of 0.0600 kg is used.(a) What is the required tension in the string? N(b) Calculate the wave speed in the string if the tension is 8.00 N. m/s
A violin string has a wave speed of 62 m/s when it isplayed. If the string is 0.60 m long and has a tensionof 200.0 N, what is the mass of the string?
A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N. If the fundamental frequency is 440 Hz, then what is the distance between the two points?
The speed of a transverse wave on a string is 110 m s−1. The tension in the string is340 N. Calculate the mass per unit length of the string
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.