lo 7/8: beats

Today on …

Physics with Patty:

BEATS!

Created by Olivia LiLO7/8 – PHYS 101 L2D

One day, Patty is practicing her violin. She is quite good at playing it and it sounds really soothing.

But her brother, Philly, just had to ruin it with his awful flute playing!

Get your flute tuned up! That awful beating is making my head throb!!

Wait, what? What beating?It’s not like I’m playing bass!

Ok, Philly. Get ready for some science. I’m talking about beats in a physical sense. It happens when two waves of different frequencies are together. For example:

This is how I sound with the violin:

This is you:

To be honest, I think I’m a much better musician than you.

Cut it out, Patty. And then?

It’s kind of pretty.

Some pulses have higher amplitudes, some have lower amplitudes, and some cancel out due to superposition of waves. But since the two waves are out of phase, something like this happens:

When graphed by itself, it looks like this!

Doesn’t it look like a DNA strand??? Doesn’t it?

The resultant amplitude modulation, or a sinusoid, has an frequency that is much lower than the average frequency of two waves combined.

Mathematically, the two waves can be written like this:

When combined in the case of superposition:

This gives us the product of 2 oscillating cosine waves, in which one oscillates at the mean angular frequency, ϖ, and the other at angular frequency difference, Δω.

Anyways. This is what is making my head throb. Better tune your flute now, kiddo.

Ugh, fine.

Thank you for watching this week’s “Physics with Patty”!

*disclaimer: all the graphs drawn in this presentation are in reference to each other, but not in scale.