A phone cord is 3.55 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 0.775 s. What is the tension in the cord?
To find the tension in the cord, we can use the wave speed equation:
Wave speed (v) = Frequency (f) × Wavelength (λ)
In this case, the pulse makes four trips down and back along the cord in a time of 0.775 s. This means that the pulse frequency (f) is the reciprocal of the time taken for one complete round trip:
f = 1 / (0.775 s / 4) = 5.16 Hz
Now let's calculate the wavelength. Since the pulse travels down and back along the cord, one complete round trip will cover twice the length of the cord:
Wavelength (λ) = 2 × 3.55 m = 7.10 m
Now, we can substitute the values of frequency and wavelength into the wave speed equation to find the wave speed (v):
v = f × λ = 5.16 Hz × 7.10 m = 36.636 m/s
The wave speed can also be expressed as the square root of the tension (T) divided by the linear mass density (μ) of the cord:
v = √(T / μ)
To find the tension (T), we need to determine the linear mass density (μ) of the cord. The linear mass density is equal to the mass per unit length, given by:
μ = mass / length = 0.200 kg / 3.55 m = 0.0563 kg/m
Now, we can rearrange the wave speed equation to solve for T:
T = v^2 × μ = (36.636 m/s)^2 × 0.0563 kg/m = 90.2 N
Therefore, the tension in the cord is approximately 90.2 N.