Beats (AP1)
1.
Wave A interferes with Wave B to produce the resultant Wave C. At each interval, add the amplitude of Wave A
to Wave B and create the resultant Wave C
2. Rectangular transverse wave oulses are traveling towardds eachother along a string. The grides shown in the
background are identical, and the pulses vary in height and length. The pulses will meet and interact soon after
they are int he position shown. Rank from greatest to least maximum amplitude of the string at the instant
that the position of the centers of the two pulses coincide. Justufy your ranking.
Largest amplitude:
A
>
B
>
C
>
D
smallest amplitude
3. Do interference beats have anything to do with the “beat” of music? Explain.
No, interference beats have to do with the waves from two sources interfering with
eachother. While the beat of music is what you dance to and is usually provided by the
drums.
4. Two adjacent point sources, A and B, are directly in front of an observer and emit identical 1000 Hz tones. At
what closest distance behind source B would source A have to be moved for the observer to hear no sound?
(Assume air temperature is 20oC) (0.172 m)
vsound  331
(20  273)
 343m / s
273
v  f   343  (1000)    0.343m
If speaker A is moved behind speaker B to the FIRST point (n=0) where NO SOUND is heard,
then destrictive interference must be happening, crests must be meeting troughs and the
speaker has been moved half a wavelength
1
1

r2  r1    n    (0.343)  0.172m  0.2m
2
2

5. As a person walks in between a pair of loudspeakers that produce tones of the same amplitude and frequency, he
hears a varying sound intensity. Explain.
The sound waves from the two speakers are interfering with eachother producing areas of
constructibe intererance (loud sound) and areas of destructive interference (quiet sound).
6. If the frequency of two speakers were lowered, would the points where destructive and constructive interference
occur move further apart or closer together? Explain.
If the frequency decreases, the wavelength would increase (speed stays the same). Therefore,
the areas between constructive and destructive interference occure would be more spread
apart.
7. An airplane mechanic notices that the sound from a twin-engine aircraft varies rapidly in loudness when both
engines are running. What could be causing this variation from loud to soft?
The sound waves from the two engines are interfering with eachother producing areas of
constructibe intererance (loud sound) and areas of destructive interference (quiet sound).
8. A violinist tunes her instrument by listening to the correct frequency and then adjusting the violen until she no
longer hears any beats. As the violen becomes more in tune, what happens to the beat frequency? Explain.
The beat frequency decreases until she no longer hears any beats. The difference between the
violen’s sound and the true sound decreases and that difference is the beat frequency.
9. Two tuning forks are hit at the same time. One has a frequency of 630 Hz and a beat frequency of 13 Hz is heard.
What two possible frequencies could the other tuning fork have?
fb  f 2  f1
13  630  f1  617  620Hz
13  f1  630  643  640Hz
10. A G can either have a frequency of 384 Hz while an F has a frequency of 341.3 Hz. If played together, what beat
frequency will be heard?
fb  384  341.3  42.7  42 Hz
fb  f 2  f1
11. Two identical point sources are generating waves witht he same frequency and amplitude. The two sources are in
phase with eachother so the two sources generate wave crests at the same instant.
a. The wavelength of the waves is equal to the distance between the two sources. Fill out the table
describing each labeled point as hearing constructive or destructive interference and then explain why.
Constructive
Destructive
Interference
Interference
X
A
B
X
C
X
D
X
E
X
The difference in path length between each speaker and the given points is either one wavelength or a whole
number or wavelengths (For example: Point A: r1 = 2 boxes, r2 = 4 boxes; r2-r1 = 2 boxes or one wavelength)
b. The distance between the two sources is equal to one and one-half the wavelength (1.5). Fill out the
table describing each labeled point as hearing constructive or destructive interference and then explain
why.
Constructive
Interference
A
Destructive
Interference
X
B
X
C
X
D
X
E
X
F
X
The difference in path length between each speaker
and the given
points is either half a wavelength or a whole number plus half a wavelength (For example: Point A: r1 = 2 boxes, r2
= 5 boxes; r2-r1 = 3 boxes or 1 ½ wavelengths)