Physics P
Worksheet
19.1a
Worksheet 19.1a Interference of Waves
Interference of Waves
1. A tuning fork emits sound at a frequency of 1000 Hz from each of the tines that are separated by
2 cm. As the tuning fork is rotated, it is observed that the volume of the sound increases and
decreases. Explain why this happens.
2. Two speakers placed 4 m apart both emit sound at a frequency of 250 Hz (assume the speed of
sound to be 340 m/s). If you are standing equidistant from both speakers and 10 m away from their
center you are at the central maximum. How far to one side would you need to walk to find the 1st
order maximum?
3. Light from a HeNe laser with a wavelength of 632.8 nm is incident upon a screen with two narrow
slits separated by a distance of 0.2 mm. What is the spacing between the bright spots projected on a
wall 10 m away?
4. What will be the spacing if the experiment in #3 is repeated with a YAG laser with a wavelength of
472 nm?
5. A radio station broadcasts at a frequency of 88.1 MHz using two towers separated by a distance of
400 m and positioned so that one tower is due north of the other. As you drive north at 90 km/h
(25 m/s) along a highway that is 50 km east of the towers, how often does the signal fade to a
minimum?
6. A laser beam is incident upon two narrow slits. At a distance of 5.0 m, it is observed that the spacing
between the interference maxima is 1.5 cm. The wavelength of the light from the laser is 500 nm.
What is the spacing between the slits?
7. Two speakers are located on one wall of a room and separated by 6 m. At the center of the wall 5 m
away you find the central interference maximum and 2 m away you find the 1st order maximum.
What is the wavelength of the sound coming from the speakers? What is its frequency?
8. Light of wavelength 500 nm in air strikes a double slit. The distance between the slits is 0.4 mm.
Bright and dark fringes are observed on a screen 2 m away from the slits.
(a) Calculate the distance between two adjacent bright fringes on the screen.
(b) The entire double-slit apparatus, including the slits and the screen, is submerged in water, which
has an index of refraction 1.33. Determine the wavelength for this light in water.
(c) State whether the distance between the fringes on the screen increases, decreases, or remains the
same. Justify your answer.
Physics P
Worksheet 19.1a Interference of Waves
1.
At some angles the wave meet up in phase resulting in constructive interference, at other
angles they meet up out of phase resulting in destructive interference.
2.
v = fλ
v
λ=
f
340$m/s
λ=
250$Hz
λ = 1.36$m
xd
L
λL
x=
d
1.36%m 10%m
x=
4%m
x = 3.4%m
λ=
(
3.
)(
xd
L
λL
x=
d
632.8&nm 10&m
x=
0.2&mm
x = 0.032&m
= 32&mm
λ=
(
4.
)
)(
)
xd
L
λL
x=
d
472$nm 10$m
x=
0.2$mm
x = 0.024$m
λ=
(
= 24$mm
)(
)
Physics P
5.
Worksheet 19.1a Interference of Waves
v = fλ
v
f
3" × "108 "m/s
λ=
88.1"MHz
λ = 3.41"m
λ=
xd
L
λL
x=
d
3.41%m 50%km
x=
400%m
x = 426%m
λ=
(
)(
)
Δd
Δt
Δd
Δt =
v
426$m
Δt =
90$km/h
Δt = 0.0047$h
v=
=17$s
6.
xd
L
λL
d=
x
500#nm 5.0#m
d=
1.5#cm
x = 1.7# × #10−4 #m
= 0.17#mm
= 170#µm
λ=
(
)(
)
Physics P
7.
Worksheet 19.1a Interference of Waves
λ=
λ=
xd
L
2"m 6"m
( )( )
5"m
λ = 2.4"m
v = fλ
v
λ
340$m/s
f=
2.4$m
f = 142$Hz
f=
8a.
xd
L
λL
x=
d
500#nm 2#m
x=
0.4#mm
x = 0.0025#m
λ=
(
)( )
= 2.5#mm
8b.
n=
n=
n=
c
v
f λv
f λw
λv
λw
λv
n
500#nm
λw =
1.33
λw = 376#nm
λw =
8c.
The fringes will get closer together.
xd
L
λL
x=
d
376$nm 2$m
x=
0.4$mm
x = 0.0019$m
= 1.9$mm
λ=
(
)( )
Physics P
Worksheet 19.1a Interference of Waves