# Why does it do that?

1. Nov 20, 2004

### billy_boy_999

when i'm stirring sugar into my coffee, the tone of the stirring sound gets higher and higher pitched...if you pay attention, it takes a while and it raises a lot but eventually it seems to hit a ceiling...what's going on exactly? i'm guessing that the sugar dissolving is raising the pitch somehow and that the top pitch is correspondent to the sugar being entirely dissolved...but why should that change the pitch of the sound of the stirring? how does it work?

2. Nov 20, 2004

### Mk

Hmmm, that happens when I'm making chocolate milk out of hershey's chocolate syrup and milk as well... I've never thought about it though.

3. Nov 20, 2004

### Integral

Staff Emeritus
Here is a thread which discusses this phenomena at some length.

4. Nov 20, 2004

### da_willem

The sound you hear comes from standing waves in the cup of coffee, whose frequency depends on the height of the coffe. While you stir this height remains approximately the same while the frequency definitely changes ($f=v/\lambda$). The only way this can happen is if the velocity of sound is altered.

When you stir there are a lot of small bubblues introduced in the liquid. You might reason that the new velocity of dsound in the coffe will be someweher in between that of the velocity of sound in water and in air. But the cute thing is, because of the bubbles; the fluid is much easier to compress, yielding a larger velocity.

A larger velocity means a larger frequency because of the standing waves condition. This also explains why instant coffee works much better than normal coffee or tea.

5. Nov 20, 2004

### Mk

But wouldn't since there's air in it, the sound travel slower?

6. Nov 20, 2004

### da_willem

No; the wavelength of the sound waves is much larger than the bubble size, so they 'see' the coffee with bubbles as a continuum. So the reasoning: the travels a while trough the coffee, then it slows down in a bubble etc so the velocity most be lower than in pure coffee - does not hold.

The velocity of sound in a liquid is approximately

$$1/\sqrt{\frac{\partial \rho}{\partial p}}$$.

And this quantity is actually larger for the mixture with bubbles than in pure coffee. This can be easily seen: $\sqrt{\frac{\partial \rho}{\partial p}}$ is smaller for the mixture because under the influence of pressure the density changes more than it would in pure coffee. This is because air is far easily compressed than water.