Chapter 16: Waves
A Wave is a means of transferring energy from one place to another
Transverse waves
A Transverse wave is a wave where the direction of vibration is perpendicular to the direction in which the wave travels.
Examples
1. Light waves.
2. Radio waves.
3. Waves on a rope.
4. Water waves.
Longitudinal Waves
A Longitudinal Wave is a wave where the direction of vibration is parallel to the direction in which the wave travels.
Examples
1. Sound waves in a solid, liquid or gas.
2. Compression waves on a spring.
Terms used to describe a wave
The wavelength of a wave is the distance from one point on the wave to the corresponding point on the next cycle.
The frequency of a wave is a measure of the number of oscillations (vibrations) of the wave per second*.
The periodic time of a wave (T) is the time taken for one complete cycle.
Variable Symbol Unit Symbol for unit
Frequency f Hertz Hz
Wavelength (“lamda”) metres m
Velocity v (or c for light) metres/second m/s
Periodic Time T second s
Relationship between frequency, velocity and wavelength Relationship between Periodic Time and frequency*
See Worked Problems 1 – 4, page 178, then try Questions 1 – 7, 9 - 11 (page 178/179).
Characteristics of a wave
1. Reflection is the bouncing of waves off of an obstacle in their path.
2. Refraction is the changing of direction of a wave as it travels from one medium to another.
Note that when a wave travels from one medium to another its frequency does not change*
3. Diffraction is the spreading of waves around a slit or an obstacle.
This effect is only significantly noticeable if the slit width is approximately the same size as the wavelength of the waves*.
4. Interference*
Interference occurs when waves from two sources meet to produce a wave of different amplitude.
Constructive Interference occurs when waves from two coherent sources meet to produce a wave of greater amplitude.
(Constructive interference occurs when the crests of one wave are over the crests of another wave).
Destructive Interference occurs when waves from two coherent sources meet to produce a wave of lower amplitude.
(Destructive interference occurs when the crests of one wave are over the troughs of the second wave.
This will happen if one wave is half a wavelength out of phase with respect to the other).
Coherent Waves*: Two waves are said to be coherent if they have the same frequency and are in phase.
“In phase” means crests stay over crests and troughs stay over troughs.
Stationary waves
Stationary waves are formed when two periodic travelling waves of the same frequency and amplitude, travelling in opposite directions, meet.
From the diagram we can see that:
1. The distance between two consecutives nodes is /2
2. The distance between two consecutive antinodes is /2
3. The distance between an anti-node and the next node is /4
(“nodes” = “no” movement)
See problems 5 and 6, page 185, 186. Then try Exercise 16.2, page 186.
The Doppler Effect
The Doppler Effect is the apparent change in the frequency of a wave due to the relative motion between the source of the wave and the observer.
Consider a source S emitting a wave with crests 1, 2, 3 as shown.
The distance between successive crests is the same; therefore the number of crests that pass point A in one second will correspond to the frequency of the wave.
These waves will pass over an observer in equal intervals of time.
This means that the wavelength and therefore the frequency will be the same.
In this case the source is moving to the right while emitting the waves.
The result is that:
1. Ahead of the moving source, the crests are closer together than crests from the stationary source would be. This means that the wavelength is smaller and the frequency is greater.
2. Behind the moving source, the crests are further apart than crests from the stationery source would be.
3. This means the wavelengths are greater and therefore the frequency is less.
Formula:
f” = apparent frequency
f = actual frequency
c = speed of the wave
u = speed of the moving source
Remember that the sign below the line is minus if the source is moving towards the observer – ‘Minus Is Towards’ (MITS)
See problems 7, 8, 9, page 188, 189. Then try Questions 1 – 7, page 190.
Applications of the Doppler effect:
1. Police speed traps
2. Measuring the red shift of galaxies in astronomy*
3. Ultrasound (blood movement or heartbeat of foetus)
4. Weather forecasting.
Note:
The noise from a racing car as it approaches and then moves away from an observer is an example of the Doppler effect.
But it is not an application!!
The Doppler Effect – Exam questions
Note that when explaining the effect, the marking scheme looks for four separate points here:
1. A series of non-concentric circles.
2. Direction of motion of source and position of observer must be indicated.
3. Reference to apparent change in wavelength.
4. Reference to resulting apparent change in frequency.
Leaving Cert Physics Syllabus
Content Depth of Treatment Activities STS
1. Properties of waves. Longitudinal and transverse waves: frequency, amplitude, wavelength, velocity.
Relationship c = f λ
Appropriate calculations. Everyday examples, e.g.
• Radio waves
• Waves at sea
• Seismic waves
2. Wave phenomena Reflection. Refraction. Diffraction. Interference. Simple demonstrations using slinky, ripple tank, microwaves, or other suitable method.
Stationary waves; relationship between inter-node distance and wavelength.
Diffraction effects
• at an obstacle
• at a slit
with reference to significance of the wavelength.
3. Doppler effect Qualitative treatment.
Simple quantitative treatment for moving source and stationary observer. Sound from a moving source.
Appropriate calculations without deriving formula. Red shift of stars.
Speed traps.
