2. 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.
3. 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
4. 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
5. Mathematics
Consider they’re in one dimension
Two waves of the same amplitude, different
frequencies, different wavelength, different
wave numbers
7. 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