1) Beats are caused by the constructive and destructive interference of two sound waves with slightly different frequencies over time. 2) When two waves of the same amplitude but different frequencies combine, their amplitudes will alternately add up (constructive interference) and cancel out (destructive interference) as the waves shift in and out of phase with each other. 3) This results in a waveform whose amplitude varies over time, producing a periodic variation in loudness known as beats.

1. BEATS
Learning Object (LO8)
Naysilla Dayanara - L2H

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

6. Applying the principle of superposition

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

8. Resultant Wave
Purple wave: Resultant Amplitude
Dashed line: Envelope
Time
Amplitude