Calderglen High School
WAVE PROPERTIES
SUMMARY NOTES AND
HOMEWORK.
Wave Properties.
v = wave speed (m/s or ms-1)
A = amplitude (m)
A = amplitude (m)
λ = wavelength
(measured in metres.)
Quantity and symbol
Description
Units of measurement
Amplitude A
Height of the maximum
disturbance from the zero
position.
metres (m)
Frequency f
Wavelength λ
Number of waves passing a
point each second
Distance from one point on
wave to same point on the
next.
Wave speed v
Distance covered by the wave
each second.
Period T
Time for one wave to pass
Hertz (Hz)
metres (m)
metres per second (m/s or ms-1)
Seconds (s)
Wave Formulae.
Distances are measured in
Wave speed is measured in
metres.
speed = distance ÷ time
metres per second
Times are measured in
seconds.
d
v
t
wavelength = distance ÷ Number of waves
Wavelength is measured in
meters.
d
λ
The number of waves has no
units of measurement
N
Frequency is measured in
frequency = 1 ÷ period
Hertz.
Period is measured in
seconds.
1
f
T
wave speed = frequency x wavelength
v
f
λ
Homework – unit conversions
Change these distances into
metres:
working
answer
working
answer
working
answer
12 km
5 km
375 km.
Change these times into
seconds:
20 minutes
1.5 hours
3hours 20minutes
Change these speeds into
metres per second:
2 km/hr
60 km/hr
0.2km/hr
Homework – scientific notation/prefixes
Put these quantities into standard form
34 km
9000 km
2 km
4 500 000 km
7 340 000 km
300 000 km
1 cm
20 cm
60kHz
200kHz
360MHz
16.4MHz
23GHz
300GHz
5000 mHz
160 mHz
Complete the table with the missing entries.
PREFIX
ABBREVIATION
ACTION
SCIENTIFIC NOTATION
Giga
x 1,000,000
x103
kilo
m
micro
÷ 1,000,000,000
Homework - Waves
Complete the following questions showing all working and include units where appropriate.
1. In a research laboratory water waves are generated in a tank. During one test a wave
travels along the tank at 2.5 metres per second as shown below.
1.8 metres
30 metres
a. Calculate the amplitude of the wave shown.
b. Calculate the wavelength of the wave shown.
c. Calculate the frequency of the wave shown.
2a.
A blackbird can sing notes of three different frequencies. What is meant by the term
frequency?
b.
The speed of sound is 340m/s. Calculate the wavelength of a 200 Hz signal.
c.
If the blackbirds song is heard by a hill walker 3 seconds later. Calculate the distance
between the bird and the person.
3.
Calculate how long it will take waves travelling at 35ms-1 to travel a distance of 1000m.
4a.
Explain what is meant by the frequency of a wave.
b.
Name the units used to measure frequency?
5.
Explain what is meant by the wavelength of a wave.
6.
Calculate the speed of a wave if it travels 40m in 5 s.
7.
Calculate the speed of a wave of frequency 20Hz and wavelength 2.5m.
8.
How long will it take a wave travelling at 15ms-1 to move 120m?
9.
A wave has a period of 0.002s calculate its frequency.
Energy transfer in waves.
The majority of people will immediately think about the Sea or Loch or some other body of water
when considering waves. This is useful since the effect of the wave is clearly visible on the water
surface. In Physics waves are defined as a mechanism of energy transfer.
Each energy type moves (propagates) it energy from one place to another by waves – heat wave,
light wave, sound wave, electrical and so on. Water waves are mechanical waves; as the wave
moves along its direction of travel the energy it carries can be seen to physically move (displace)
the water surface.
Water particles do not get pushed along with the wave, they are moved up and down from their
zero position as the wave passes by.
You can prove this for yourself the next time you are beside water throw a stick
into the water and then throw a stone close to it. The ripples from the stone will
make the stick bob up and down but the stick will not get carried along with the
ripples!
Tsunamis and seismic waves produced by earthquakes are extreme examples of energy transfer by
waves.
All waves with the EXCEPTION of SOUND transfer energy in this way; at RIGHT ANGLES to the
direction of travel they are called.
SOUND waves are different the energy IS transferred ALONG the direction of travel they are called
Speed of Sound.
There are a number of methods that can be used to measure the speed of sound in air; two are
described, the important thing to remember is the actual quantities measured and the name of the
instrument used to make each measurement. (e.g. distance – metre stick , tape measure etc.)
Echo method.
The time t between the clap and the
echo returning is measured with a
stopwatch
d
The distance to the wall is measured using a trundle wheel.
Remember the actual distance travelled by the sound is double this (2d)
The experiment should be repeated a number of times to allow an average time to be calculated.
Then the results are used in the formula
sound in air.
to get an approximate value for the speed of
Electronic method
A more accurate method involves the use of electronic timing. Human reaction time is eliminated
from the measurements giving a more accurate result. Microphones or sound switches are used to
start and stop a timing program on a computer (we use a dedicated TSA computer designed
specifically for physics experiments).
d
Microphone 2.
Microphone 1.
TSA
(time-speed-acceleration) computer





The distance d is measured using a metre stick.
A sound is produced at a location such that it reaches microphone 1. first.
The TSA starts recording the time.
The sound reaches microphone 2. and stops the timer.
The TSA records the time t for the sound to travel between the microphones.

Speed of sound is calculated using
.
You must be able to:
Explain how this equipment can be adapted to measure the speed of sound
in liquids and solids.
State that sound is vibrations of particles and can travel through solids,
liquids and gases but not a vacuum.
Speed of Sound Homework.
1. A pupil reads about an experiment that can be carried out to measure the speed of
sound in air. When the hammer hits the metal block a sound wave is produced. The
computer is used to measure the time it takes for the sound wave to travel from one
microphone to the other. The computer will display the time taken for the sound to
travel this distance or it can be used to calculate the speed of sound directly.
interface
microphone 2
microphone 1
computer
hammer
2.00 m
The pupil carried out the experiment, and the time measured was 0.006 s.
(a)
What other information does the computer need to calculate the speed of sound for
her?
(b)
Find the speed of sound using the pupil's results.
(c)
The pupil found that the speed was not calculated properly when the
experiment was done close to a wall. Suggest a reason for this.
2.
You see a flash of lightning, and then hear the thunder 6 seconds later. How far away
(roughly!) is the thunderstorm? Take the speed of sound to be 340ms-1.
3.
A person at the mouth of a cave shouts, and hears an echo from the back wall of the cave.
Using a stopwatch, she times 1 second between shouting and hearing the echo. Calculate
how far away the back wall of the cave is. Take the speed of sound to be 340 ms-1.
4.
Complete the following table. You must show all your working for each answer.
speed
10 ms
distance
time
-1
100 m
3000 m
1.2 m-1
150 s
30 s
Sound properties.
Glossary of equipment
SIGNAL GENERATOR.
These come in various styles but they all
essentially perform the same function.
They produce a PURE electrical signal,
one whose frequency and amplitude can be
changed. When the signal is applied to a
loudspeaker it produces a sound wave of
the same frequency and amplitude.
LOUDSPEAKERS
These devices convert electrical
energy into sound energy
DECIBEL METER / SOUND LEVEL METER
Used to measure the relative volume of a sound in
decibels.
CATHODE RAY OSCILLOSCOPE
(CRO)
Oscilloscopes give a visual display of
electrical signals. When a signal generator is
connected to an oscilloscope it allows us to
‘see’ the sound wave being produced.
Sound Level.
The following experimental set up can be use to determine the relationship between sound level
(volume) and the amplitude of the sound wave. Examples of oscilloscope traces for loud and quiet
sounds are given. Complete the diagram with the correct equipment names.
LOUD SOUND
QUIET SOUND
LARGE AMPLITUDE
SMALL AMPLITUDE
Noise Pollution.
DESCRIPTION OF SOUND
SOUND LEVEL
Threshold of Hearing (TOH)
Rustling Leaves
Whisper
Normal Conversation
Busy Street Traffic
Vacuum Cleaner
Pneumatic drill
iPod at Maximum Level
Front Rows of Rock Concert
Threshold of Pain
Military Jet Takeoff
Instant Perforation of Eardrum
0 dB
10 dB
20 dB
60 dB
70 dB
80 dB
90 dB
100 dB
110 dB
130 dB
140 dB
160 dB
NUMBER OF TIMES LOUDER
THAN 0dB.
1
x2
x4
x 64
x 128
x 256
x 512
x 1024
x 2048
x 4096
x 8192
X 16384
The table above show some sounds for comparison with a typical volume level in decibels (dB). The
decibel scale is differently from linear scales such as those used to measure temperature or
distance. An increase of 10dB means the sound has doubled in perceived volume. So a vacuum
cleaner sounds twice as loud as a busy street and so on. Sounds of 90dB and over are classified as
Noise Pollution because they can be harmful.
The internal ear is a sensitive organ with delicate membranes, nerves and cilia which can be
damaged by excessive sound energy. Temporary damage can occur from short term exposure to
very loud sounds, permanent damage can result from long term exposure to sounds of 85-90dB.
However these are not the only sound level conditions that can result in hearing damage.
Employers are required by law to provide ear plugs or defenders to employees who are exposed to
sound levels of 90dB. These contain high density foam which absorbs some of the sound energy
(vibration) before it enters the ear.
Sounds and sound levels Homework.
1.
In each of the following situations, state whether the sound is travelling through a solid, a
liquid or a gas.
(a) Native Americans could hear horses a long way off by putting their ear to the ground.
(½)
(b) Dolphins use high-pitched sounds to locate fish for food.
(c) A teacher shouts at you for not attempting your homework!
(½)
(½)
2.
In the Star Wars films (and similar), there are many loud explosions as spaceships blow up.
In reality, you wouldn't hear the explosions at all. Why not?
(1)
3.
Use the figures below to estimate the typical sound level of each sound:
10 dB, 30 dB, 60 dB, 70 dB, 90 dB, 120 dB
sound
Busy street
Inside an engine factory
Heavy truck passing by
Leaves rustling in the wind
Whisper
Normal conversation at 1 metre
4.
Give two examples of noise pollution.
level
5. (a)
(b)
6.
In what way could a noisy factory cause harm to its workers?
How could the workers avoid this harm? (without quitting their jobs!)
Ear plugs and earmuffs are used to protect hearing.
(a) What do these protectors do to the sound’s energy?
(b) Suggest a material that could be used for the filling of the protectors.
7.
(1)
On the decibel scale, every 10 dB represents an effective doubling of the perceived loudness
of sounds. More simply, a sound of 50 dB will sound twice as loud to you compared to a
sound of 40 dB.
How many times louder than leaves rustling in the wind does normal conversation sound?
Use values from the table in question 3 to help you.
(1)
Frequency of sound .
We use the same apparatus as before for the
sound level experiment to look at the
relationship between the frequency and pitch
of sounds.
LOW PITCH
HIGH PITCH
SMALL FREQUENCY
LARGE FREQUENCY
Range of Hearing.
There is a limit to the highest and lowest pitched sounds that humans and animals can hear. For
humans this is typically 20Hz to 20kHz. As we age these limits will most likely change reducing our
ability to hear the low and /or high frequencies. The apparatus can be used to determine your own
range of hearing (maybe your old teacher might lend an ear too for comparison!).
Lower limit (Hz)
Me
Teacher
Upper limit (Hz)
Ultrasound.
Frequencies of 20000Hz (20kHz) and above are classified as ultrasound. Despite being beyond the
range of human hearing ultrasound has several important uses.
Like all sounds ultrasound can travel through solids, liquids and gasses and also like other sounds
the speed changes depending on the medium.
Air = 340ms-1
Soft tissue = 1500ms-1
Bone = 3400ms-1
Something else happens when ultrasound changes from one material to another. Some of the
sound gets reflected at the boundary. The reflected signal can be detected by sensitive
equipment. Using electronics these signals are converted in to an image on a computer
monitor.
ULTRASOUND
TRANSMITTER
Reflected waves
ULTRASOUND
RECIEVER
REFLECTED
SIGNAL USED
TO FORM
IMAGE
Ultrasound image
or scan.
Certain animals have been using ultrasound for thousands of years to navigate and hunt prey, long
before humans were able to exploit the technique. By timing how long it takes a pulse of
ultrasound to return it is possible to get an accurate measure of the distance to an obstruction or
meal.
d
If the time for the pulse to return equals t and the speed of sound in air is 340ms-1 then the
distance is calculated using the formula:
rearranged and considering total distance.
Sonar is a similar technique used to determine the depth of the sea bed or shoals of fish.
If an ultrasonic pulse takes 20 milliseconds to return to the boat at what depth are the fish?
vwater= 1480ms-1
depth of fish
d =½vt
d= ½ x 1480 x 20x10-3
d= 14.8m
Ultrasound Homework
1. An ultrasound pulse of frequency 8 MHz is transmitted into an expectant mother’s womb
and reflects from the baby’s bottom. The pulse echo is detected 0·08 milliseconds after
being transmitted. The speed of sound through the body tissue and fluid is 1500 ms-1.
transmitter/detector
(a)
How far does the pulse travel?
(b)
How far from the transmitter is the baby’s bottom?
(c)
Another pulse is reflected from the foot of the baby. If this reflected pulse is
detected 0·15 milliseconds after being transmitted, how far from the transmitter is
the baby’s foot?
2.
3.
During an ultrasound scan, a baby’s forehead is situated 7·5 cm from the transmitter. The
ultrasound pulse travelling at 1 500 ms-1 is reflected from the baby’s forehead.
(a)
What is the total distance travelled by the pulse?
(b)
What time elapses between the transmission of the pulse and the detection of the pulse
echo?
An ultrasound pulse is transmitted into the womb of an expectant mother and the pulse echo is
detected after a time of 0·38 milliseconds. The pulse was reflected by one of the baby’s knees
situated 28·5 cm from the transmitter. Show that the speed of sound in the womb is 1 500 ms -1.
Audacity Data Sheet
These are the notes of the C major scale, starting at middle C and going up one octave.
A
F
C
D
B
G
E
Starting with middle C here is the accepted frequency of each note.
C = 261.63Hz
D = 293.66Hz
E = 329.23Hz
F = 349.23Hz
G = 392Hz
A = 440Hz
B = 493.88Hz
C = 523.26Hz
C
Using Audacity
In audacity select generate, then tone
Start with middle C and input the frequency and duration.
Change the frequency here.
Change the duration here to
1 second.
Move the cursor to the end of the track, right click and repeat. Add all the frequencies to produce
an ascending scale.
Hit the play button to hear your masterpiece.
Below is a familiar tune, using the data sheet, input the frequencies and durations to create a piece
of music.
duration 1s
duration 2s
duration 4s
Now you can personalise you creation by adding effects to all or part of the track. Go experiment!
Don’t forget to look at how the wave form is altered when effects are added. You might want to
generate your own tune.
Finally save your finished file as an MP3, then you can upload it to your phone to use as a ring
tone.
There are almost endless possibilities regarding sound manipulation. Noise cancellation
headphones are one example. Noise is simply unwanted waves which interfere with the quality of
the audio signal such as background hiss or crackle heard when listening to poorly recorded
music. Let’s look at how they work.
Use the Audacity program to generate a tone track again: frequency = 440Hz duration 30s. Right
click on the grey area under the track you have just created then generate a second identical track.
Hit the play button to hear both tracks played
together
Right click on one of the tracks about 10s in and drag to highlight a 10s portion. Select effects and
then select invert.
Hit the play button again and notice what happens.
Zooming in to look at the waves in more detail we see
that inverting the signal turns it upside down. When
both tracks are played together the waves are added
and the inverted section combines with the noninverted signal to produce silence. Both signals are
still being played (listen to each individually if you
want) but we have effectively cancelled the output to
the speakers.
Now clear all the files from audacity then go to:
File/open/shared documents/physics/audacity samples/sample track.
This is a 6 second sample of a song which has been recorded with background interference. Give it
a listen.
Noise cancellation headphones use sophisticated electronics to identify the unwanted ‘noise’ in an
audio track, this signal is inverted and added back to the track to eliminate the unwanted signal.
We can demonstrate the effect. In the audacity samples folder are three samples of noise see if you
can find the correct noise profile, manipulate it and add it to the music file to get rid of the
unwanted noise.
Diffraction
Waves are able to bend around objects by a process called diffraction. How much they diffract
depends on the wavelength of the wave. A ripple tank can show this wavelength dependence.
Vibrating paddle
Water tank
Projected wave
pattern
Long wavelengths diffract more than short wavelengths
Complete these diagrams.
Shortwave diffraction
Longwave diffraction
Diffraction Homework.
1.
A child in the back seat of a car is watching a hand held television. The frequency of the
channel is 2000 MHz.
a.
On entering a hilly region the picture becomes distorted and eventually cannot be seen.
Explain why the television signal fades.
b.
Calculate the wavelength of the television signal.
c.
the driver of the car tries the radio, he tunes to a frequency of 1500 kHz and finds that a clear
signal is received. Explain why the radio signal can be picked up but the television signal
cannot.
d.
Show by calculation that the radio wave has a longer wavelength than the television wave.