The document discusses wave interference, outlining true statements about destructive and constructive interference with specific examples. It also presents questions regarding the conditions for constructive interference between two waves, and provides solutions that clarify the relationships between wavelength, frequency, and amplitude. Key statements indicated as correct include the properties of beat frequency and binaural beating.

1. Learning
object
March 15
15-5 >> INTERFERENCE
AND BEATS

2. Select the statements that are true
a) Destructive interference occurs when ΔD = λ/2
b) The path difference of two waves is 3λ/2. This is constructive
interference.
c) Amplitude for a spherical wave increases as r increases.
d) The beat frequency of a 120 Hz tone and a 105 Hz tone played
simultaneously is 115 Hz.
e) Two waves that start out interfering constructively and get out
of phase with each other will continue to be out of phase, thus
interfere destructively.
f) Binaural beating is independent of interference of sound waves
in our skull.
QUESTION 1

3. Two waves, both with a wavelength of 2.0 m are 3.0 m apart. Will
these two waves interfere constructively? Show your work and
support your answer with numbers.
QUESTION 2

4. What is the wavelength of spatial modulation of the amplitude of
the sum of two waves at frequencies of 250Hz and 236Hz, that are
both travelling at 340 m/s?
QUESTION 3

5. Answers a, d, and f are correct. Explanations:
a. Destructive interference occurs when the path difference is a
half-integer multiple of wavelength.
b. The path difference of 3λ/2 is a half-integer multiple, therefore it
is destructive interference, not constructive.
c. The wave front spreads out over a large area as it propagates
outward, therefore amplitude decreases as r increases.
d. The amplitude modulations of the two waves have the same
frequency as the difference between the two frequencies.
e. Two waves are able to move in and out of phase depending on
their wave functions.
f. Binaural beating results from the way our brain processes
signals from our ears.
QUESTION 1 SOLUTION

6. k = 2Π/λ
k = 2Π/2.0m
= Π
k (d2-d1) = n2Π
Π (3.0m) = n2Π
n = 3/2
No they will not interfere constructively because n is not an
integer multiple, but rather a half-integer multiple value, thus will
interfere destructively.
QUESTION 2 SOLUTION

7. Beat frequency = 250Hz – 236Hz
= 14Hz
V = λ/f
λ = v/f
= (34m/s) / 14Hz
= 2.4 m
QUESTION 3 SOLUTION