A transverse wave traveling in a string takes 1.40 s to move 13.2 m. The mass of a 8.50 m piece of the string is 1.60 kg. What is the tension in the string?
To find the tension in the string, we can use the formula for the wave speed:
Wave speed (v) = Frequency (f) x Wavelength (λ)
We can determine the wavelength by using the given information that the wave takes 1.40 s to move 13.2 m:
Wave speed (v) = Distance (d) / Time (t)
v = 13.2 m / 1.40 s
Next, we can find the frequency by using the formula for wave speed:
v = f * λ
Rearranging the formula, we get:
λ = v / f
Now, we can substitute the values we have:
13.2 m / 1.40 s = λ
Solving for λ, we find:
λ = 9.43 m
Now that we have the wavelength, we can calculate the wave speed:
v = 13.2 m / 1.40 s = 9.43 m/s
Finally, we can calculate the tension in the string using the following formula:
Tension (T) = μ * v^2
Where μ is the linear mass density of the string, given by:
μ = mass (m) / length (L)
Substituting the given values, we have:
μ = 1.60 kg / 8.50 m = 0.1882 kg/m
And substituting the calculated values for wave speed and linear mass density, we get:
Tension (T) = 0.1882 kg/m * (9.43 m/s)^2
Solving the equation, we find:
Tension (T) = 16.9 N
Therefore, the tension in the string is 16.9 N.