1. Superposition of Unequal Frequency Waves
Consider two harmonic waves A and B meeting at x=0.
Same amplitudes, but 2 = 1.
The displacement versus time for each is shown below:
A(1t)
B(2t)
What does C(t) = A(t) + B(t) look like??
04/28/2003
Physics 103, Spring 2003, U. Wisconsin

2. Superposition & Interference
Consider two harmonic waves A and B meeting at x = 0.
Same amplitudes, but 2 = 1.15 x 1.
The displacement versus time for each is shown below:
A(1t)
B(2t)
CONSTRUCTIVE INTERFERENCE
DESTRUCTIVE INTERFERENCE
C(t) = A(t) + B(t)
04/28/2003
Physics 103, Spring 2003, U. Wisconsin

3. Physics 103, Spring 2003, U. Wisconsin
Beats
Can we predict this pattern mathematically?
Of course!
Just add two cosines and remember the identity:
where
and
cos(Lt)
04/28/2003
Physics 103, Spring 2003, U. Wisconsin

4. Physics 103, Spring 2003, U. Wisconsin
04/28/2003
Physics 103, Spring 2003, U. Wisconsin

5. Physics 103, Spring 2003, U. Wisconsin
Lecture 27, Preflight 5
A tuning fork has a frequency of 440 Hz. The string of a violin and this tuning fork, when sounded together, produce a beat frequency of 1 Hz. From this information is it possible to deduce the frequency of the violin string?
1. yes
2. no
correct
The beat frequency is the difference between the two frequencies of the waves, so the violin is either 441 Hz or 439 Hz. You would have to know which of the two had a greater frequencies.
04/28/2003
Physics 103, Spring 2003, U. Wisconsin

6. Physics 103, Spring 2003, U. Wisconsin
Problem 1
51. Two train whistles have identical frequencies of 180 Hz. When one train is at rest in the station, sounding its whistle, a beat frequency of 2 Hz is heard from a moving train. What two possible speeds and directions can the moving train have?
04/28/2003
Physics 103, Spring 2003, U. Wisconsin

7. Physics 103, Spring 2003, U. Wisconsin
Problem 2
48. A 2.00-m-long air column is open at both ends. The frequency of a certain harmonic is 410 Hz, and the frequency of the next higher harmonic is 492 Hz. Determine the speed of sound in the air column.
04/28/2003
Physics 103, Spring 2003, U. Wisconsin

8. Physics 103, Spring 2003, U. Wisconsin
Problem 3
24. A bat flying at 5.0 m/s emits a chirp at 40 kHz. If this sound pulse is reflected by a wall, what is the frequency of the echo received by the bat?
04/28/2003
Physics 103, Spring 2003, U. Wisconsin