General Wave Properties I
- Describing wave motion: types of waves
- Characteristics of a wave · Wave terms
- Graphs: displacementâdistance and displacementâtime
What is a wave?
- A wave is made up of periodic motion (motion repeated at regular intervals).
- It is a travelling disturbance.
- The source (origin) of any wave is a vibration or oscillation.
Wave motion can be seen in a slinky spring, a rope, a ripple tank, or water in a pond or lake.
Characteristics of waves
- â Waves transfer energy from one place to another. The kinetic energy of the moving particles (on the rope or in the water) is passed along from one end to the other.
- â Waves do not transfer matter.
Types of wave motion
Transverse waves
Waves that travel in a direction perpendicular to the direction of vibration.
e.g. electromagnetic waves such as light, microwaves and infrared, as well as a rope wave.
Longitudinal waves
Waves that travel in a direction parallel to the direction of vibration.
e.g. sound waves, or a slinky pushed and pulled along its length.
How do particles move as the wave passes?
The rope wave moves to the right. What will particles P, Q, R and S do in the next instant?
Answer
Wave terms
| Term | Meaning | SI unit |
|---|---|---|
| Crest / trough | The highest / lowest point of a transverse wave. For longitudinal waves the equivalents are compressions (like crests) and rarefactions (like troughs). | â |
| Wavelength λ | The shortest distance between any two points on a wave that are in phase, e.g. two successive crests or troughs. | metre (m) |
| Amplitude A | The maximum displacement from the rest (centre) position. It is the height of a crest or depth of a trough, measured from the rest position. | metre (m) |
| Displacement | The distance of a point or particle from its rest (equilibrium) position at that moment. | metre (m) |
| Period T | The time taken for one point on the wave to complete one oscillation. This is also the time taken to produce one complete wave. | second (s) |
| Frequency f | The number of complete waves produced per second. | hertz (Hz) |
| Wave speed v | The distance a wave travels per second. In one period T, a crest moves forward one wavelength λ. | m/s |
A wave has crests and troughs whose heights from the rest position are 0.1 m, 0.15 m, 0.2 m and 0.3 m, and the largest is labelled x.
(1) State the amplitude. (2) State x. (3) What do 0.1 m, 0.15 m and 0.2 m mean?
Answer
(2) x = 0.3 m
(3) They are the displacements of those points/particles from the rest (equilibrium) position.
A wave shows 3 complete waves across a distance of 1.0 m.
(a) How many complete waves are there in 1 m? (b) Calculate the wavelength.
Answer
(b) λ = 1.0 m ÷ 3 = 0.333 m (3 s.f.)
Displacementâdistance graph
This graph is a snapshot of the whole wave at one instant. You can read wavelength and amplitude from it.
From the graph above, state (a) the amplitude, (b) the wavelength, and (2) how many complete waves are shown.
Answer
Displacementâtime graph
This graph follows one point (e.g. point P on a rope) over time. You can read period and amplitude from it, and then use f = 1/T.
It takes 0.04 s to produce two complete waves and the wavelength is 3 m. Calculate the speed.
Answer
v = λ / T = 3 / 0.02 = 150 m/s
A displacementâtime graph has peaks at ±3.0 cm and one complete wave every 0.5 ms. State the (a) amplitude and (b) period, then (2) calculate the frequency.
Answer
(b) T = 0.5 ms = 5.0 Ă 10â»âŽ s
(2) f = 1 / (5.0 Ă 10â»âŽ) = 2000 Hz
A displacementâtime graph peaks at 0.1 cm and one full wave takes 0.1 s. State (1) the amplitude and (2) the period, and (3) find how many complete waves form in one second.
Answer
Wavefronts
Circular wavefronts in a ripple tank travel at 6.0 cm/s. The distance from X to Y (between consecutive wavefronts) is 0.80 cm. (a) State the wavelength. (b) Calculate the frequency.
Answer
(b) f = v / λ = 6.0 / 0.80 = 7.5 Hz
General Wave Properties II: Sound
- How sound is produced and travels (compressions and rarefactions)
- Transmission and speed of sound in different media
- Echoes and their uses · Pitch and loudness
What is sound?
- Sound is a form of energy.
- It is passed from one point to another as a wave.
- It is an example of a longitudinal wave.
How is sound produced?
Sound is a longitudinal wave created by a vibrating source, such as a tuning fork or a drumstick hitting a drum, placed in a medium (solid, liquid or gas).
The vibrating source shifts layers of air particles back and forth. For example, striking a tuning fork and dipping it into water makes the water splash.
How does sound travel?
The air molecules vibrate parallel to the direction of wave motion. As a tuning fork vibrates, it shifts layers of air inward and outward, which creates a series of compressions (C) and rarefactions (R).
Compression (C)
A region of high density of air, where particles are close together, which means high pressure.
This forms when the prongs push outward.
Rarefaction (R)
A region of low density of air, where particles are far apart, which means low pressure.
This forms when the prongs move inward.
- The air pressure rises above the surrounding air pressure and then falls below it. This continues as long as sound is produced.
- C to the next C (or R to the next R) is one wavelength, and C to the adjacent R is half a wavelength.
Transmission of sound
Can sound travel through a vacuum? No.
This can be proven with the bell jar experiment:
- An electric bell hangs inside a sealed jar. When it is switched on, the striker hits the bell and a sound is heard.
- Air is pumped out of the jar. As a vacuum forms, the sound becomes fainter and fainter.
- Finally, you can still see the striker hitting the bell, but no sound is heard.
Speed of sound in different media
| Medium | State | Approx. speed (m/s) |
|---|---|---|
| Air | gas | 300 |
| Water | liquid | 1500 |
| Iron | solid | 5000 |
| Granite | solid | 5400 |
Sound travels fastest in solids because the particles are closely packed in the solid state.
Reflection of sound: echoes
An echo forms when sound is reflected off hard, flat surfaces, such as a large wall or a distant cliff.
Echoes obey the laws of reflection: the angle of incidence i equals the angle of reflection r. With a barrier between two cardboard tubes, the ear hears the reflected sound loudest when i = r.
Uses of echoes
For example, finding the depth of the sea.
A ship sends out a pulse of sound to find the sea depth and the position of shoals of fish.
Bats and dolphins use it to locate distant or invisible objects.
Sonar waves are sent from the bottom of a ship to find the depth of the sea. The echoes return 0.8 s after emission. The speed of sound in water is 1200 m/s. Calculate the depth.
Answer
d = (1200 Ă 0.8) Ă· 2 = 480 m
A girl stands 150 m in front of a tall building and fires a starting pistol. A boy standing 350 m behind her hears two bangs 1.0 s apart. Calculate the speed of sound in air.
Answer
Extra distance = 650 â 350 = 300 m, covered in 1.0 s
v = 300 / 1.0 = 300 m/s
A man near a cliff shouts and hears two echoes, 2.8 s and 3.6 s after the shout. The speed of sound is 300 m/s. (a) Draw the two likely paths. (b) Calculate the distances of the two reflecting surfaces from him.
Answer
(b) Path 1: 2d = 300 Ă 2.8 â d = 420 m
Path 2: 2d = 300 Ă 3.6 â d = 540 m
Pitch and loudness
High pitch = high frequency · Low pitch = low frequency
e.g. a 200 Hz sound has a higher pitch than a 100 Hz sound.
Larger amplitude = louder sound · Smaller amplitude = softer sound
The window shows 10 ms of the sound. Higher frequency packs in more waves (higher pitch), and a bigger amplitude gives taller waves (louder).
The diagrams show the wave patterns of four sounds, all on the same time scale.
(Ex 5) Which sound has the highest pitch? (Ex 7) Which has the lowest pitch and is loudest?
Answer
Ex 7: D, because it has the fewest waves (lowest frequency) and the largest amplitude.
A graph shows a waveform with period 2 s. Draw the waveform with (a) twice the frequency and (b) half the frequency.
Answer
(a) twice: f = 2 Ă 0.5 = 1 Hz (T = 1 s, one complete wave in 1 s)
(b) half: f = 0.25 Hz (T = 4 s)
Electromagnetic Waves
- State that all electromagnetic waves are transverse waves that travel with the same speed in a vacuum
- Describe the main regions of the EM spectrum in order of wavelength and frequency
What are electromagnetic waves?
Characteristics of EM waves
| # | All EM waves⊠|
|---|---|
| â 1 | are transverse waves |
| 2 | are made up of oscillating electric and magnetic fields. They do not carry electric charges. |
| â 3 | travel at 3 Ă 10âž m/s in a vacuum |
| 4 | obey v = fλ |
| â 5 | slow down when they pass from a vacuum into another medium: speed and wavelength decrease, but the frequency stays the same as at the source. |
| 6 | undergo reflection and refraction |
| 7 | transfer energy |
The electromagnetic spectrum
R M I V U X G: Radio · Microwaves · Infrared · Visible light · Ultraviolet · X-rays · Gamma rays
5G technology
Singapore and many other countries see fifth generation (5G) wireless technology as a driver of economic growth. 5G uses EM waves in the GHz range instead of the MHz range, so it can transfer data about a thousand times faster than 4G.
Uses of radio waves (longest λ, lowest f)
- Communication
- The police and military each have their own assigned radio frequency bands.
- Communication links between ground stations and satellites have their own allocated frequencies.
- Radio waves in the 3â30 MHz range are reflected repeatedly off the ionosphere and the ground, so they can travel thousands of km. This makes them very useful for long-distance communication.
- Radio & TV broadcasting: each station has its own assigned frequency band. When you tune in, sound is encoded and sent through the air to your radio set.
- Radio Frequency Identification (RFID): an RFID tag is a small, thin circuit that holds identification data.
Radio telescopes can be connected together to give higher resolution images.
Uses of microwaves
- Cooking: the energy transferred increases the internal energy of the food, which raises its temperature.
- Communication: satellite communication and mobile phones. (These use microwaves, not radio waves!) A phone converts sound into microwave signals, which go to a cell tower. The receiving phone converts them back into sound. Wi-Fi also uses microwaves, at about a thousand times less power than a microwave oven.
- Radar (Radio Detection and Ranging): the time taken for emitted microwaves to be reflected back by an object is used to calculate the object's distance.
- Cancer treatment: microwaves can be used to kill cancer cells.
- GPS: microwave signals from at least three satellites let a receiver (a GPS device or phone) work out its location.
Uses of infrared
We feel warm near a fire, even without touching it, because our skin has thermoreceptors that are sensitive to infrared.
- Cooking / keeping warm: the heated rods in ovens and electric heaters give out infrared.
- Data transfer: between devices such as phones and laptops. IR has a higher frequency than microwaves, so it can carry more data, faster. This is why it is used in long-distance fibre-optic cables.
- Remote controls: for example, for a TV or air-conditioner.
- Camera auto-focusing: the camera emits IR that bounces off the subject and uses the same principle as radar to work out the distance.
- IR thermometers & intruder alarms: these detect the infrared given off by a person, for example to measure body temperature.
- Greenhouses: they trap long-wavelength IR to keep the inside warm enough for plants to grow.
Uses of visible light
Visible light is essential for people and animals to see.
- Photography: a digital camera uses a sensor to record an image.
- Artificial light for plant growth
- Telecommunication & medicine: light is reflected repeatedly inside a thin optical glass fibre. An endoscope uses this to look inside hollow organs, and it is also used in laparoscopy ('keyhole' surgery).
- Hardening / curing materials: for example, dental fillings.
- Chemical reactions: photographic films are coated with chemicals that react to light and record an image.
Uses of ultraviolet
- Disinfection & sterilisation: kills bacteria and viruses, for example in Singapore's water treatment plants and on the travellator and escalator handrails at Changi Airport (UV-C LEDs).
- Vitamin D production: the right dose of UV from the sun helps the body make vitamin D, which is good for bones, muscles and the immune system. Sun-tanning beds also use UV.
- Anti-forgery: pigments that glow under UV are used as security features on bank notes.
Also at Changi: the proximity touch screens at check-in kiosks use infrared sensors, so they work without being touched.
Uses of X-rays
- X-ray imaging: different tissues let different amounts of X-rays through. Parts that absorb more (such as bone) appear brighter, which reveals fractures and cancerous growths.
- CT scan: combines X-ray images taken at different angles to form a detailed image.
- Security scanning: airport luggage is scanned for hazardous materials.
- Quality control: manufactured goods are scanned for hidden defects and cracks.
Uses of gamma rays (shortest λ, highest f, highest energy)
- Disinfection & sterilisation: like UV and X-rays.
- Quality control: manufactured goods are scanned for hidden defects and cracks.
- Radiotherapy: kills cancer cells. The Gamma Knife focuses many beams on one point, which gives high precision and fast recovery.
Summary table
| Wave | Typical λ | Key uses |
|---|---|---|
| Radio | m to km | Communication, radio/TV broadcasting, RFID |
| Microwaves | ~cm | Cooking, satellites & mobile phones, Wi-Fi, radar, GPS, cancer treatment |
| Infrared | ~10 ”m | Heaters, remote controls, fibre-optic data, auto-focus, thermometers, alarms |
| Visible | 400â700 nm | Seeing, photography, optical fibres/endoscopes, curing, plant growth |
| Ultraviolet | ~10 nm | Sterilisation, vitamin D, anti-forgery |
| X-rays | ~0.1 nm | Medical imaging, CT, security, quality control |
| Gamma | < 0.01 nm | Sterilisation, quality control, radiotherapy |
Quick check
Try to answer each one before you open it.
1. State the difference between a transverse and a longitudinal wave.
Answer
2. Define wavelength.
Answer
3. A wave has f = 50 Hz and λ = 4 m. Find v and T.
Answer
4. Why does sound travel fastest in solids?
Answer
5. An echo returns 1.5 s after a clap (v = 330 m/s). How far away is the wall?
Answer
6. Light passes from a vacuum into glass. What happens to its speed, wavelength and frequency?
Answer
7. List the EM spectrum from lowest to highest frequency.
Answer
8. Which EM wave is used for mobile phones and satellite communication?