A phone cord is 4.25 m long. The cord has a mass of 0.200 kg. A transverse wave pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in 0.780 s. What is the tension in the cord?
To find the tension in the cord, we can use the formula for the wave speed, which is given by:
v = 2L / T
Where:
- v is the wave speed
- L is the length of the cord
- T is the time it takes for the pulse to make a round trip along the cord.
In this case, we are given the length of the cord (L = 4.25 m) and the time it takes for the pulse to make four trips (T = 0.780 s / 4).
First, let's calculate the time it takes for the pulse to make one round trip along the cord:
T_single_trip = T / 4 = 0.780 s / 4
Next, we can substitute the known values into the wave speed formula:
v = 2L / T_single_trip
Now we have the wave speed (v), which is determined by the tension in the cord, and the length of the cord (L). We can rearrange the formula to solve for the tension (T):
T = 2L / v
Finally, we substitute the values into the equation to find the tension in the cord:
T = 2(4.25 m) / v
Therefore, to find the tension in the cord, we first need to calculate the wave speed using the formula v = 2L / T_single_trip, and then substitute the wave speed into the equation T = 2L / v.
The wave speed is
v = 2*4*4.25/0.78 = 43.5 m/s
The mass per unit length of the cord is a = 0.04706 kg/m
The wave speed is related to tension force T by the equation
v = sqrt(T/a)
Solve for T
T = a v^2 = 89 Newtons