Learning Objective 7 - Beats

1. Learning Objective:
Haitian Zou
35281147
Mar.15, 2015

2. Problem about beats
Question:
A tuning fork and a piano emit f1 =
480 Hz and f2 = 484 Hz,
respectively. What do you hear?

3. What is “beat” ?
- Constructive and destructive interference
separated by intervals of time
When listening to two waves with
slightly difference in frequencies, we
hear the amplitude increasing and
decreasing as a function of time.

4. Beats
Consider two waves that have the same
amplitude but different frequencies
and
Set both phases to be zero and consider the
resultant amplitude at a fixed position in space
x=x0.
Then we get the two equations:
(from textbook, p436)
1
2

5. Beats
(From textbook p.436)
Apply the principle of
superposition and ad
the two waves.

6. Beats
If we simplify the complicated calculations, we
can get the following two equations:
Mean angular frequency
Angular frequency difference

7. Important concepts about Beats
beat frequency ( fB )
When there are two similar frequencies ( f1 , f2), a third
much lower frequency is heard at the same time.
This frequency is called the beat frequency ( fB ).
f1-f2=fB

8. Important concepts about Beats
combined frequency( fC)
This is the result of superposition of the two
original frequencies. The combined frequency is
simply the average of these frequencies.
fc=(f1+f2)/2

9. Beats
After knowing the basic ideas, we can solve the
problem given at the beginning of the slides
A tuning fork and a piano emit f1 = 480
Hz and f2 = 484 Hz, respectively.
What do you hear?

10. Problem about beats
Answer:
A sound at 482 Hz with 4 beats
per second.

11. Explanations
Because 480Hz and 484Hz are similar frequencies,
they result a superposition. The combined
frequency will simply the average of the two
frequencies.
The answer should be (480Hz+484Hz)/2=482Hz
· A sound at 482 Hz

12. Explanations
· 4 beats per second
480Hz and 484Hz are two similar frequencies.
This the beat frequency is heard at the same time.
Here, the beat frequency is 484Hz-480Hz=4Hz

13. Summary of the class
This class we talked about constructive and
destructive interference related to intervals of
time. Two new concepts are introduced – beat
frequency (fB)and combined frequency(fc).
We learnt two new equations:
f1-f2=fB
fc=(f1+f2)/2

14. Thank you!
This is the end of the class.