# Why does a skipping rope produce sound when going suffciently fast?

I was wondering how exactly sound waves are produced by a skipping rope. Specifically a plastic one, but I think it should occur in all materials.

There are two possible explanations I can think of:

1. The rope travels through the air fast enough, to push the air molecules out of the way, thereby creating a compression wave. And another one when the molecules slam together behind the rope.
2. The friction of the rope with the air creates the sound (how?).

Are these perhaps even the same? I'm not sure about how I'd go about exploring the validity of these hypotheses.

• Possibly the result of a Kármán vortex street behind the rope: Wikipedia Mar 12, 2017 at 10:16

Sound generated aerodynamically is a mature topic. There are some relevant lecture notes here: http://people.bath.ac.uk/ensmjc/Notes/tnoise.pdf (Although if you have access it's worth your while to read Lighthill's 1952 account).

In essence, correlations of Reynolds stresses (recall a stress is just a flux of momentum) due to regular fluctuations or turbulence in the flow can be shown to be equivalent to a distribution of acoustic quadrapoles, hence generating sound.

If you want a heuristic understanding then it's worth going through the thought experiment of sound generation due to a pulsating sphere. The velocity field of the fluid is related to the pressure through the Navier-Stokes equations. It can then be shown that fluctuations of the momentum imparted by the pulsating sphere to the fluid drives a pressure field and therefore sound is created.

• That sounds interesting but is a couple notches too advanced for me to understand. Can you dumb it down a bit? Mar 12, 2017 at 15:06
• @bitmask Take a look at this brilliant video (watch the whole series, while you're a it ;)) and then we can discuss in more detail: youtube.com/watch?v=8BmESsMroRM Mar 12, 2017 at 18:06
• Why do acoustic quadrapoles generate sound? :P Mar 13, 2017 at 22:03

I am not very sure about this, but I found something you might like. When air (especially turbulent air) passes over an obstacle, eddies are generated. These eddies produce a low continuous tone. For a cylindrical obstacle, the frequency is given by:

$f = \frac{\alpha.v}{d}$ where $v$ is the air velocity near the obstacle surface, $\alpha$ is the Strouhal Number~0.2 (see Strouhal Number), and $d$ is the diameter of the cylinder.

For a skipping rope, it acts as a cylinder cutting through the air, so relative to the rope, the air is turbulent around it and the previous equation apply (statistically). For more see Aeolian Sound.

Lets assume a skipping rope in a shape of rotating parabola fixed at two ends by the hand gripp, rotating at an angular speed that accelerates and decelaretes according to its position either climbing arc or descending arc with no tugs.

the front surfaces of the rope which is a half cylinder will sweep and collect some molecules of air and build a wedge of compressed air while the back has created a vacuum.

The front wedge will collaps with spilling of the air when the pressure is enough to give super critical speed to air molecules to scape and go around to the low pressure area in the back.

This rapid build up if pressure and decompression is one source of ropes sound.

The interaction of this paraboloid wave- front with its own wake after every turn makes additional harmonies.

Interaction if this wave with ground gives it a beat effect.

On the other hand there is air that clings and washes along the length of the rope until it gets ejected into vibrating snake looking shock waves in the air.

This is a very intuitive non technical and incomplete picture of the mechanics of the phenomenon.

Just as I can hear you breath and your vocal chords vibrate to produce your voice.

A rope makes sound being whipped thru the air (air resistance)

When the rope hits the floor when you skip your stricking it with enough speed and force that it bounces off it and you can see the shockwave briefly in the (temporarily) deformed rope misdoing.

See below video

Slow Mo up Close Jumprope