# Does friction slow down a wave (in a phone cord among others)?

1. Feb 22, 2014

I'll pose that as a general question, and specifically for sound waves, which Googling did not answer in a satisfactory way.

And a specific instance I'm concerned with is as follows:
- Students are using telephone cords to make waves (cheaper and much more durable than Slinkies!).
- Most groups hold the cord stretched through the air.
- But one group put the cord on the floor, and snapped it sideways to generate a wave.

Especially at higher amplitudes (more sideways) the cord rubs a lot on the floor. We are debating, to no conclusion: does that friction affects the measured speed of the pulse?

2. Feb 22, 2014

### Staff: Mentor

I would expect this, but not as a strong effect.

Something that certainly influences the propagation speed is the tension of the cord (if there is tension at all).

3. Feb 22, 2014

### AlephZero

There will be tension if the cord was suspended in the air, unless the cord is weightless!

The speed will depend mainly on two things, the tension in the cord and its own flexibility, acting like a coil spring.

There will be smaller effects from the amplitude of the waves (a bigger amplitude causes more "stretching" of the length of the cord) and the amount of damping.

For a damping force proportional to velocity, the frequency is reduced from $\omega$ to $\omega\sqrt{1 - \beta^2}$ where $\beta$ is a measure of the amount of damping. Even if $\beta$ is quite large, for example 0.14 (which would mean the wave amplitude would be halved in about one cycle or one wavelength) the frequency change is only about 1%.

Actually, if the only source of damping is Coulomb friction (a constant force in the opposite direction to the velocity), the friction does not change the frequency at all. But that is probably an over-simplified model of your "cord on the floor" experiment.

4. Feb 22, 2014

### Staff: Mentor

Sure, but in the scenario where the cord lies on the floor it can be without tension.