Download here: Ontario Curriculum Expectations
I love to think of nature as an unlimited broadcasting station, through which God speaks to us every hour, if we only will tune in.
George Washington Carver
Vocabulary
Periodic Motion: motion that repeats itself over a regular period of time; the hands of a clock, the rotation of the Earth, and a merry-go-round all exhibit periodic motion.
Cycle: a repeated pattern. For the hand of a clock and a merry-go-round, one cycle would be a complete 360° rotation. For the rotation of the Earth, one cycle would be from the point when the sun is just about to rise until it is just about to rise the following day.
Period: the length of time for one cycle to occur. We use the symbol “T” for period and it is generally measured in seconds, though often other units may be more convenient. The period of a merry-go-round is about 10 seconds; the period of a minute hand on a clock is one hour, or 60 minutes; the rotation of the Earth has a period of one day, or 24 hours.
Frequency: is a measure of how often, or how frequently, an event occurs. We use the symbol “f” for frequency and it is measured in Hertz (Hz).
Calculating Period and Frequency
Example 1
A bird flaps its wings 24 times in 6.0 seconds. With what period and frequency is the bird flapping its wings?
Given:
?t = 6.0 s
N = 24
Required:
f = ?
T = ?
Period can be calculated using the equation: 
, where T = period (s), ?t = time interval (s), and N = the number of cycles that have occurred.
The period of each wing flap is 0.25 s.
Frequency can be calculated using the equation: 
.
The bird is flapping its wings with a frequency of 4 Hz.
Notice that the equations for period and frequency are inverses of each other.
This means that 
and 
.
Practice Questions
A child swinging on a swing set goes back and forth 24 times in one minute.a) Describe the path of the swing that makes up one cycle.
b) Determine the frequency of the child’s motion.
c) Determine the period of the child’s motion.
Answer
) Using the position of the swing h, where it is hanging still and nobody is using it as the starting point, one cycle would be made up of the child swinging forwards, all the way backwards, and then forwards to the starting point again. Any motion continuing past this point would be part of the second cycle.
Given:
N = 24
?t = 1 minute = 60 s
Required:
- f = ?
- T = ?
Solution:
b) 
c) 
or 
The child’s swinging has a period of 2.5 s and is occurring at a frequency of 0.4 Hz.
Kinds of Waves
A wave is a disturbance in a medium that transmits energy by means of a vibration. It is very important to recognize that in a wave it is the energy of vibration that is moving. The medium does not actually move from one place to another.
Transverse Waves:
In a transverse wave, the vibrations are perpendicular to the direction in which the wave is moving.
Transverse waves can clearly be seen in this video. You can see that the wave moves from left to right but the medium (the blue dots) move up and down.
The rest, or equilibrium, position is the position the medium would be in if it was not vibrating. This is shown as a black line in the diagram below.
Two points are said to be “in phase” with each other when they are both at the same point in their vibration at the same time, both going up, or both at their peak. A wavelength is the distance between two adjacent points that are vibrating in phase with each other. The wavelength is shown in orange on the diagram below. The Greek letter lambda, ?, is used as the symbol for wavelength.
The amplitude is the maximum distance the wave gets from its rest position. It is shown in purple on the diagram.
A crest occurs above the equilibrium position, shown in green, and a trough occurs below it, shown in red. A wavelength is made up of a crest and a trough.
Water waves on the ocean are an excellent example of transverse waves. While the wave moves towards the shore, the water itself only moves up and down.
Longitudinal Waves:
In a longitudinal wave, the vibrations are parallel to the direction in which the wave is moving.
Longitudinal waves can clearly be seen in this video. You can see that the wave moves from left to right and so does the medium.
A longitudinal wave is made up of a series of compressions, where the particles in the medium are compressed together, and rarefactions, where the particles in the medium are stretched apart. As with a transverse wave, a wavelength is the distance between two adjacent points that are vibrating in phase with each other. A wavelength is made up of one compression and one rarefaction.
Earthquakes and sound waves are excellent examples of longitudinal waves.
View how the particles in a medium move as a wave passes through them. Try to follow the path of any one of the grey dots. You will see that it only moves up and down while the wave itself moves left to right across the screen.
This video allows you to see the motion of a transverse wave and a longitudinal wave at the same time.
The Universal Wave Equation
The universal wave equation applies to all waves, everywhere. It states that 
where v is the speed of the wave (m/s), ? is the wavelength (m), and f is the frequency (Hz).
For instance, by counting how many troughs pass a given point in a 20 s time interval you can determine the frequency of the wave. If the speed of the wave increases so that it is moving to the right at a much faster rate, more troughs will pass that point in the 20 s time interval. This means that the wave will have a higher frequency.
Similarly, if the wavelength is made much shorter, the distance between troughs will be smaller and they will be closer together. This will also increase the frequency with which troughs are passing a given point.
These two relationships can be combined into one statement to form the universal wave equation.
Example 2
A sound wave travelling through the air has a speed of 330 m/s. If the sound has a frequency of 2.4 kHz, what is its wavelength?
Given:
v = 330 m/s
f = 2.4 kHz = 2400 Hz
Required:
? = ?
Solution:
The sound has a wavelength of about 14 cm.
Practice Questions
- An earthquake travels at 3.8 km/s and has a wavelength of 480 m. What is the frequency of the earthquake?
Answer
Given:
v = 3.8 km/s = 3800 m/s
? = 480 m
Required:
f = ?
Solution:
The frequency of the earthquake is 7.9 Hz.
2.
- How many cycles are shown in the diagram?
- Is this a transverse or longitudinal wave?
- What is the wavelength of the wave shown?
- What is the amplitude of the wave shown?
- If the period of the wave is 1.50 s, what is its speed?
Answer
- 3.5 cycles
- Transverse wave
- ? = 27/3 = 9 cm
- amplitude = 20/2 = 10 cm
- Given:
T = 1.5 s
? = 9 cm
Required:
f = ? (to use in the universal wave equation)
v = ?
Solution:
v = ?f = (9 cm)(0.67 Hz) = 6 m/s
The speed of the wave is 6 m/s.