Example
Which type of wave requires a material medium to travel
through?
a) Television
b) Light
c) Sound
d) Radio
e) X-ray
Sound is a mechanical wave,
and mechanical waves require a
medium to travel through.
Example
A periodic wave transfers?
a) Mass and Energy
b) Mass only
c) Energy only
d) Neither Mass and Energy
e) Sound
Light, does not have mass, or sound
effects, but any periodic wave does
transfer energy, since energy was given
to it to make it oscillate
Example
A periodic wave is produced when you hit one of the prongs
of a tuning fork. To increase the amplitude of the wave, you
would need to:
a) Hit the prong harder
b) Hit the prong faster
c) Hit the prong slower
d) Nothing, amplitude it fixed
e) Shorten the prong
When you hit the fork harder, you are
transferring more energy to the fork,
increasing the amplitude of the wave
Example
What is the period of a 50-Hz electromagnetic wave
travelling at 3x108 m/s?
a) 20s
b) 2s
c) 0.2s
d) 0.02s
e) 0.002s
1
1
T 
 0.02s
f 50 Hz
Example
A periodic wave with a frequency of 10 Hz and a speed of
20 m/s has a wavelength of:
a) 20m
b) 2m
c) 0.2m
d) 0.02m
e) 0.002m
m
v
s  2m
 
f 10 Hz
20
Example
An electromagnetic wave with a wavelength of 2.0x10-1 m
is travelling through a vacuum, What is its period?
a) 20s
b) 5s
c) 3.0x108s
d) 2.0x10-1s
e) 6.7x10-10s


2.0  10 1 m
v  f  T  
 6.7  10 10 s
T
v 3.0  108 m
s
Example
The phenomenon that cause sound waves to shatter a
glass cub is?
a) Reflection
b) Refraction
c) Resonance
d) Diffraction
e) Interference
Example
If you have two waves travelling in the same medium with the
same frequency and amplitude. The maximum destructive
interference will occur when the phase difference between
the two waves is:
a) 0o
b) 90o
c) 180o
d) 270o
e) 360o
Example
When tuning a piano, a key produces a note of 150 Hz,
when the next key is hit a beat pattern twice a second is
heard. What could the frequency be for the second out of
tune key?
a) 152 Hz
b) 75 Hz
c) 300 Hz
d) 148 Hz
e) 2 Hz
fbeat  f2  f1
Example
Two children create a standing wave when skipping. If the
children are 4.60 metres apart, then determine the
wavelength of this standing wave.
a) 9.20 m
b) 4.60 m
c) 1.50 m
d) 13.8 m
e) 2.30 m
This standing wave is ½ of the actual
wavelength
Example
You design a string instrument in which the speed of the
travelling waves are 400m/s. How long should the string
be to produce the first fundamental frequency at 300Hz.
a) 1.42 m
b) 0.42 m
c) 1.50 m
d) 1.8 m
e) 0.67 m
v
n
f
L

2
2
n
Hint:
m

1  400 

nv
s

L

 0.67m
2f
2  300 Hz 
Example
You are given a 1m length of rope and you record the
velocity of a pulse along this rope as 400 m/s. What
frequency or frequencies could not be produced by the
rope.
a) 200 Hz
b) 400 Hz
c) 500 Hz
d) 600 Hz
e) 1200Hz
Hint:
200 Hz is the fundamental frequency (or first
harmonic), 400 Hz is the Second Harmonic (or
first overtone), 600 Hz is the 3rd Harmonic (or
second overtone, and 1200 Hz is the fourth
Harmonic (or 3rd overtone).
nv
f 
2L
Example
You are given four organ pipes with standing waves of the
air displacement. Given that the speed of sound is 343 m/s.
2m
a) Which pipe has the
highest frequency and
what is that frequency
b) Which pipe has the
lowest frequency and
what is that frequency
c) Which pipe has the
longest wavelength
and what is that
wavelength
d) Which pipe has the
shortest wavelength
and what is that
wavelength
Example
You are given four organ pipes with standing waves of the
air displacement. Given that the speed of sound is 343 m/s.
a) Which pipe has the highest frequency and what is that frequency?
b) Which pipe has the lowest frequency and what is that frequency?
2m
nv
4L
f 
f 
f 
f 
nv
4L
nv
4L
nv
2L
f 
f 
f 
f 
 5  343
m

s
 214 Hz
 3  343
m

s
 129 Hz
1  343
m

s
 42.9 Hz
 3  343
m

s
 257 Hz

4  2m 

4  2m 

4  2m 

2  2m 
Example
You are given four organ pipes with standing waves of the
air displacement. Given that the speed of sound is 343 m/s.
c) Which pipe has the longest wavelength and what is that wavelength
d) Which pipe has the shortest wavelength and what is that wavelength
2m
4L

n

 4  2m   8 m
4L
n

 4  2m   8 m
4L

n

2L

n


5
3
5
3
 4 2m   8m
1
 4  2m   8 m
3
3
Example
You have a pipe that is closed at one end and open at the other.
A tuning fork resonates when the pipe is 11 cm long. The same
tuning fork does not resonate at any pipe smaller than this. At
what other pipe length with the tuning fork resonate?
a) 22 cm
b) 33 cm
c) 44 cm
d) 55 cm
e) 66 cm
Solution
You have a pipe that is closed at one end and open at the other.
A tuning fork resonates when the pipe is 11 cm long. The same
tuning fork does not resonate at any pipe smaller than this. At
what other pipe length with the tuning fork resonate?
11 cm
The wavelength
of the wave then
must be 44 cm
Since the pipe is
open at one end and
closed at the other it
has a node at the
closed end and a antimode at the other
The next harmonic oscillation occurs when
there again is a anti-node at the open end,
or 3 x 11cm = 33cm
Example
An ambulance’s siren produces a sound wave of constant
frequency. As the ambulance accelerates away from you,
you notice that the sound wave:
a) Increases in amplitude and decreases in frequency
b) Increases in amplitude and increases in frequency
c) decreases in amplitude and decreases in frequency
d) decreases in amplitude and increases in frequency
e) Remains fixed in amplitude and decreases in frequency
Because the ambulance is moving away, the
frequency of the wave is decreasing, plus the
sound gets lower in volume, so the amplitude
also decreases.
Example
You inhale some helium, as a result, the pitch of your
voice rises. What happens to the standing waves of your
vocal cords to cause this effect
a) The frequency of the waves decrease
b) The speed of the waves decrease
c) The speed of the waves increase
d) The wavelength of the waves decrease
e) The wavelength of the waves increase
Since the pitch of your voice increases, the frequency
must increase. The wavelength does not change
(wavelength depends upon physicsal structure of your
voice box). Therefore by v=λf, the speed of the waves
must increase. (the speed of sound in helium is faster
than in air)
Example
A siren is emitting sound at a frequency of 1500Hz and an
observer is moving away from the siren at 100 m/s. Given
that the speed of sound in the air is 340 m/s, determine
the observed frequency of the siren.
 v  v0 
Hint: f   f 

 v  vs 
m
m

 340 s  100 s 
f   1500 Hz 

m


340
s


 12 
f   1500 Hz  
 17 
Since you and the source are
moving away from each other, the
frequency must be lower
f   1060 Hz
Example
A rope is tied between two poles that are 8 m apart. Give
two allowed standing wavelengths for this rope.
Hint:
2
n  L
n
2
1   8m 
1
 16m
2
 8m 
2
 8m
2 
Use this formula for Fixed-Fixed
conditions
Example
The distance between two successive nodes in a
vibrating string is 10cm. Given that the frequency of the
source is 30 Hz. What is there wavelength?
Hint:
d node
1
 
2
1
10cm  
2
  20cm
Example
A lightning flash is seen in the sky and 8.2 seconds later the
boom of thunder is heard. The temperature of the air is 12.0
C.
(a) What is the speed of sound in air at that temperature?
v   331  0.606TC  m/s
The speed of sound in
air of this temperature
is 338 m/s.
(b) How far away is the lightning strike?
d  vt
  338 m/s  8.2 s 
 2800 m
 2.8 km
Example
The speed of light is 3.00105 km/s. How long does it take
the light signal to reach the observer?
d
t
v
2.8 km

3.0  105 km/s
 9.3  10 6 sec
Example
Two wave pulses with amplitude A are travelling towards
each other along a rope. When they interfere, what is the
maximum amplitude of the resulting collision when the
wavelength of one wave is twice the wavelength of the
other?
AT  A1  A2
 2A
Wavelength plays no role
in determining the
resultant amplitude.
Example
Given that a human’s ear vibrates with an amplitude of
2.0x10-10 m. when listening to a 4 kHz sound. What is the
total distance will the eardrum move in 1 minute?
Hint:
Find number of cycles in 1 minute
cycles 

cycles   60 s   4000

s 

 240000
d  2  2.0  10 10 m   240000 
 9.6  10 5 m
Example
A sound wave in air moves at a speed of 340 m/s. Which is
the closest to the wavelength of middle C (f=256 Hz)
v

f
m
340
s

256 Hz
 1.33m
Wavelength plays no role
in determining the
resultant amplitude.