A transverse wave traveling in a string takes 1.61 s to move 13.2 m. The mass of a 9.2 m piece of the string is 1.5 kg. What is the tension in the string?
To determine the tension in the string, we can use the formula for the speed of a transverse wave on a string.
The wave speed (v) can be calculated using the equation:
v = √(T/μ)
where:
v is the wave speed,
T is the tension in the string,
and μ is the linear mass density of the string.
First, we need to calculate the wave speed using the given information. The wave speed (v) can be calculated by dividing the distance traveled by the time taken:
v = distance / time
Given:
distance = 13.2 m
time = 1.61 s
v = 13.2 m / 1.61 s
v ≈ 8.2 m/s
Next, we need to calculate the linear mass density of the string (μ). The linear mass density (μ) can be calculated by dividing the mass of the string by its length:
μ = mass / length
Given:
mass = 1.5 kg
length = 9.2 m
μ = 1.5 kg / 9.2 m
μ ≈ 0.163 kg/m
Now we have all the required information to find the tension in the string (T):
T = v^2 * μ
Substituting the values we have:
T = (8.2 m/s)^2 * 0.163 kg/m
T ≈ 10.889 N
Therefore, the tension in the string is approximately 10.889 N.