Sound Waves Traveling Down a String

Part A = 0.26 s

Solution Below:

Part A

If the string is 9.5 m long, has a mass of 55 g and is pulled taut with a tension of 7.5 N, how much time does it take for a wave to travel from one end of the string to the other?

Express your answer using two significant figures.

Express your answer using two significant figures.

Let’s start with what we already know. Velocity equals distance divided by time:

v = d/t

What you may or may not have learned in your class is that for traveling waves, velocity is proportional to the square root of the force divided by the medium’s linear density (μ). The linear density is just the mass per unit length. So we end up with:

v = d/t

d/t = sqrt(F / μ)

9.5/t = sqrt(7.5 N / (0.055 kg / 9.5 m))

9.5/t = sqrt(7.5 / 0.005789)

9.5/t = sqrt(1296)

9.5/t = 36

t = 0.26 seconds

0.26 s