Question

A 25 g string is under 20 N of tension. A pulse travels the length of the string in 50 ms. How long is the string?

Short answer

The length of the string is 2 meters

Step-by-step solution

Step 1.  Write the given information

The mass of the string is m = 25g = 0.025kg

The tension of the string is T = 20N

The traveling time for the wave is t = 50ms

Step 2. To determine the length of the string

The speed of the wave is given by the expression
$$\begin{gathered} v=\sqrt{\frac{T}{m}L} \\ \Rightarrow \frac{L}{∆t}=\sqrt{\frac{T}{m}L} \end{gathered}$$
squaring on both the sides
$$\begin{gathered} \frac{L^2}{{\left(∆t\right)}^2}=\frac{T}{m}L \\ \Rightarrow L=\frac{T}{m}{\left(∆t\right)}^2 \end{gathered}$$

substitute the known values
$$\begin{gathered} \Rightarrow L=\frac{20N}{0.025kg}{\left(50\times {10}^{-3}sec\right)}^2 \\ L=2m \end{gathered}$$

Thus the length of the string is 2 meters