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Chapter 16: Waves Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier.
The speed of sound is 340 m s- The speed of light is 3 × 10^8 m s-
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
- Light waves.
- Radio waves.
- Waves on a rope.
- 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
- Sound waves in a solid, liquid or gas.
- 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 (^) λ (“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*
v = f λ (^) T = 1/f
Characteristics of a wave
- Reflection is the bouncing of waves off of an obstacle in their path.
- 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*
- 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 *.
- 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:
- The distance between two consecutives nodes is λ/
- The distance between two consecutive antinodes is λ/
- The distance between an anti-node and the next node is λ/
(“nodes” = “no” movement)
Leaving Cert Physics Syllabus
Content Depth of Treatment Activities STS
- 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
- 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.
- 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.
Extra Credit Earthquakes and Waves Earthquakes and violent volcanic eruptions are a source of seismic waves that result in planet Earth ringing like a bell for quite some time (up to weeks) after the "striking" event. Less dramatically, the Earth "hums" all of the time with a collection of frequencies in the 1 to 10 mHz range. This frequency translates into a period of typically 200s, which gives a clue to its origin. Many sea-borne waves near to continental land masses (infragravity waves) have periods of this order of magnitude. It is the interaction of these waves in the shallower water over continental shelves with the seabed that drive the "hum". Most sea waves originate in the action of winds over the water surface. In their turn winds derive their energy from the Sun's unequal heating of the Earth's surface and atmosphere. So the Earth is humming to the tune of the Sun. Reference: Nature 15th^ February pp754-756.
*The frequency of a wave is a measure of the number of oscillations (vibrations) of the wave per second. Another way of defining frequency of a wave is to say it is the number of waves that pass a fixed point per second. This second definition is helpful in explaining the next point: T = 1/f
*Relationship between Periodic Time and frequency T = 1/f or f = 1/T If three waves pass a fixed point per second (f = 3 Hz), it follows that the time for one wave to pass (periodic time T) is 1/3 (seconds). Alternatively if the Periodic Time (T) is 1/5 seconds, it follows that five waves will pass in one second (f = 5 Hz).
*When a wave travels from one medium to another its frequency does not change Basically if a wave ‘wobbles’ so many times a second in air, and then comes in contact with another medium e.g. water, the water will ‘wobble’ (move in and out) in sympathy with the driving force, and therefore at the same frequency. The speed however will change, and because speed is directly proportional to wavelength (from v = fλ), if the speed of the wave were to double (and the frequency remains constant) then the wavelength would double also. *Diffraction is the spreading of waves around an obstacle This effect is only significantly noticeable if the slit is approximately the same size as the wavelength of the waves. So if the slit width is of the order of cm to metres, then sound may well be noticeably diffracted, depending on the frequency of the sound, because the corresponding wavelength may well be similar to the slit width. However the same will not happen for light, because the wavelength for light is of the order of 10-7^ metres, which doesn’t correspond to slits that one encounters every day. There are objects which are specifically designed to have these slit widths specifically so that light will diffract after passing through them. These are called ‘Diffraction Gratings’ and we will use them when studying Chapter 18: The Wave Nature of Light. Similarly, compact dics have grooves in them which are approximately the same width as the wavelength of light, so shining white light on a CD gives a nice spectral pattern! So why is the effect only noticeable when the wavelength is the same size as the gap? Answer: I don’t know. If you can explain it or find someone else who can, please get back to me. I suspect it is another of those concepts which is a lot more technical than it first appears. But then maybe I just think that to make me feel better
*Interference Interference is considered to be the most significant of the four characteristics because if a form of energy undergoes interference then it must be a wave (as opposed to travelling as particles). We know that both sound and light travel as waves because we can show that they undergo interference.
*Coherent Waves Strictly speaking the definition is a little more convoluted: Two waves are said to be coherent if they have the same frequency (or wavelength) and are in phase (or have a constant phase difference between them) Another necessary condition (for waves to be coherent) is therefore that both waves travel at the same speed.
- Applications of the Doppler effect: Measuring the red shift of galaxies in astronomy Strictly speaking the red-shift is due to two separate factors; other galaxies moving away from us and the fact that the space itself is expanding (our universe is expanding), so the distance between crests is increasing and this would happen even if the galaxies were not speeding away from us.
