BEATSLearning Object (LO8)

Naysilla Dayanara - L2H

DEFINITION

Constructive and Destructive interference separated by

intervals of space

Constructive and Destructive interference separated by

intervals of time

What we hear when this happens: Variation of amplitude

as a function of time.

FIRST, CONSIDER THIS…2 waves of the same amplitude

Have slightly different frequencies: Say that they are f1 and f2.

f1

f2

Time

Checkpoint: Think about the loudness

FIRST, CONSIDER THIS…

Time

f1

f2

At first they’re in phase:Therefore they ADD UP Eventually gains up and

becomes one half cycle out of phase

Therefore, they CANCEL OUT

WHAT WILL THIS SOUND LIKE??

The result is a wave with different amplitudes

MathematicsConsider they’re in one dimension

Two waves of the same amplitude, different frequencies, different wavelength, different wave numbers

Applying the principle of superposition

Now we have a product of two cosines:

Oscillates at mean angular frequency

Oscillates at angular frequency

difference

We hear a tone that has: Mean Frequency

Amplitude varies by the difference in angular frequency

Resultant WavePurple wave: Resultant Amplitude

Dashed line: Envelope

Time

Ampli

tude