Wave Model

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Notes de leçon

Properties of Travelling Waves

Travelling waves are oscillations that transfer energy from one place to another without transferring matter.
Waves are generated by oscillating sources; the oscillations travel away from the source.
Oscillations can propagate through a medium (e.g. air, water) or in a vacuum (no particles), depending on the type of wave.
Key properties of travelling waves: displacement, wavelength, amplitude, period, frequency, wave speed.

Displacement, Wavelength and Amplitude

Displacement x is the distance of a point on the wave from its equilibrium position; it is a vector (can be positive or negative) and is measured in metres (m).
Wavelength \lambda is the length of one complete oscillation, measured from the same point on two consecutive waves (e.g. crest to crest or trough to trough); measured in metres (m).
Amplitude A is the maximum displacement from the equilibrium position (x = 0); it can be positive or negative and is measured in metres (m).
The horizontal line where the wave has zero amplitude is the equilibrium position.

Diagram showing wave crest, trough, resting position, wavelength, and amplitude

Period, Frequency and the Wave Equation

Period T is the time taken for one complete oscillation to pass a fixed point; measured in seconds (s).
Frequency f is the number of complete oscillations passing a fixed point per second; measured in Hertz (Hz).
Frequency and period are related by f = \frac{1}{T}.
Wave speed v is the distance travelled by the wave per unit time; measured in metres per second (m s⁻¹).
The wave equation is v = f\lambda = \frac{\lambda}{T}.
For a wave of constant speed: as wavelength increases, frequency decreases; as wavelength decreases, frequency increases.

Interpreting Wave Graphs

If the x-axis is time, the distance for one full wave is the period T.
If the x-axis is distance, the distance for one full wave is the wavelength \lambda.
Always convert units: for frequency in Hz, the period must be in seconds (not milliseconds or microseconds).
Amplitude is read from the vertical axis as the maximum displacement from the equilibrium position.

Transverse Waves

Transverse waves have oscillations perpendicular to the direction of motion and energy transfer.
Particles in a transverse wave vibrate up and down.
Transverse waves show areas of peaks (crests) and troughs.
Examples: electromagnetic waves (radio, visible light, UV) and mechanical waves (e.g. vibrations on a guitar string).
Transverse waves transfer energy even if there is no resultant displacement of the medium; they do not need particles to propagate, so they can travel through a vacuum.

Longitudinal and transverse waves.

Longitudinal Waves

Longitudinal waves have oscillations parallel to the direction of motion and energy transfer.
Particles in a longitudinal wave vibrate left and right (back and forth along the direction of travel).
As a longitudinal wave propagates, areas of high pressure (compressions) and low pressure (rarefactions) are observed.
A compression is where particles are closer together; a rarefaction is where particles are further apart.
Examples: sound waves and ultrasound waves.
Longitudinal waves are mechanical waves; they need particles to propagate and cannot travel through a vacuum.

Longitudinal wave motion

Sound Waves

Sound waves are longitudinal and require a medium to propagate.
They are generated by oscillating sources that produce a change in density of the surrounding medium, travelling as a series of compressions and rarefactions.
Sound waves form a continuous spectrum based on frequency.
Humans can hear frequencies in the range 20 Hz – 20 kHz (the audible range).
Pitch is related to frequency: high pitch = high frequency (short wavelength); low pitch = low frequency (long wavelength).
Volume is related to amplitude: large amplitude = high volume; small amplitude = low volume.
Speed of sound in air at room temperature is about 340 m s⁻¹; it increases with air temperature because the average kinetic energy of particles is higher.
Sound travels fastest through solids (particles closely packed) and slowest through gases (particles spread out).

Pitch and amplitude of sound waves

Electromagnetic Waves

An electromagnetic wave is generated by the combined oscillation of an electric field and a magnetic field.
These fields oscillate perpendicularly to each other and to the direction of motion (energy transfer).
Electromagnetic waves are transverse and can travel through a vacuum.
All electromagnetic waves travel at the speed of light c = 3 \times 10⁸ \text{ m s}^-1 in a vacuum, regardless of frequency.
They form a continuous spectrum based on frequency (or wavelength).
The shorter the wavelength (or higher the frequency), the greater the energy of the wave.
Humans can only sense wavelengths in the range 700 nm – 400 nm (the visible spectrum).
Frequencies can be calculated using the wave equation c = f\lambda with c = 3 \times 10⁸ \text{ m s}^-1.

The electromagnetic spectrum, showing the seven regions in order of decreasing wavelength (increasing frequency), from radio waves to gamma rays.

Mechanical vs Electromagnetic Waves

Mechanical waves require a medium (fluid or solid) to propagate; they can be transverse or longitudinal; they cannot travel through a vacuum.
Electromagnetic waves do not require a medium; they are only transverse; they can travel through a vacuum.
Mechanical waves are produced by the oscillation of particles in a medium; electromagnetic waves are produced by oscillating charged particles.
Examples of mechanical waves: sound waves, water waves, seismic waves. Examples of electromagnetic waves: radio waves, UV rays, X-rays.
Mechanical waves travel much slower than the speed of light; electromagnetic waves travel at the speed of light.

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1.Which statement does not describe a property of travelling waves?
Easy
- AEnergy and matter are transferred by travelling waves
- BThe direction of motion of a travelling wave is the direction of energy transfer
- CTravelling waves travel away from the source of oscillation
- DThe oscillations can propagate through a medium or in a vacuum depending on the type of travelling wave
2.Identify the correct units for the quantities in the wave equation v = fλ.
Easy
- AWave speed: m s⁻², Frequency: J, Wavelength: m
- BWave speed: m s⁻¹, Frequency: Hz, Wavelength: m
- CWave speed: m s⁻¹, Frequency: Hz, Wavelength: s
- DWave speed: m s⁻¹, Frequency: Hz, Wavelength: m²
3.A sound wave has a frequency f of 50 Hz. Identify the correct expression showing the time period T of the wave.
Easy
- AT = 50
- BT = 1/50
- CT = 1/(2×50)
- DT = 2×50
4.Identify the example that is not a transverse wave.
Easy
- ASound wave
- BMicrowave
- CWater wave
- DSunlight
5.Which of the following gives regions of the electromagnetic spectrum in order of increasing frequency?
Medium
- AGamma ray, visible, radio wave
- BX-ray, microwave, ultraviolet
- CRadio wave, infrared, microwave
- DInfrared, ultraviolet, x-ray
6.An electromagnetic wave is generated by combined oscillations of electric and magnetic fields. These fields oscillate perpendicular to each other and to the direction of motion. In a diagram, if the electric field oscillates in plane P, which labels correctly identify Q and R?
Medium
- AQ: Motion, R: Magnetic field
- BQ: Electric field, R: Motion
- CQ: Magnetic field, R: Electric field
- DQ: Magnetic field, R: Motion
7.Which of the following has a frequency lower than that of visible light?
Easy
- AUltraviolet
- BInfrared
- CGamma ray
- DX-ray
8.Which frequency of sound wave would a human be able to hear?
Easy
- A2 Hz
- B200 Hz
- C200 kHz
- D2000 kHz

Plus de questions

9.Which of the following sound waves would give the highest volume?
Easy
- AA wave with small amplitude
- BA wave with large amplitude
- CA wave with high frequency
- DA wave with low frequency
10.Which of the following sound waves would produce the highest pitch?
Easy
- AA wave with high frequency
- BA wave with low frequency
- CA wave with large amplitude
- DA wave with small amplitude
11.A radio station broadcasts in the frequency range 97–99 MHz. What range of wavelengths are being used?
Medium
- A3.3 – 3.9 × 10⁻⁹ m
- B3.03 – 3.09 × 10⁻⁶ m
- C3.03 – 3.09 m
- D0.33 – 0.39 × 10³ m
12.A longitudinal travelling wave has speed v and wavelength λ. What is the least distance between a compression and a rarefaction measured along the direction of propagation?
Medium
- Av/λ
- Bλ
- Cλ/2
- D2λ
13.A sound wave has a wavelength of 0.40 m. What is the phase difference between two points along the wave which are 1.7 m apart?
Medium
- Azero
- B45°
- C90°
- D180°
14.Two waves are travelling from the surface of the Sun to the upper atmosphere of Earth. Which statements must be correct? I. The waves have the same frequency II. The waves have the same speed III. Neither wave is longitudinal IV. At least one of the waves is audible to humans
Hard
- AI and II
- BI, II and III
- CII and III
- DI and IV
15.A section of the electromagnetic spectrum is shown with four labelled regions I, II, III, IV in order of decreasing frequency. What could the labelled sections represent?
Medium
- AI: ultraviolet, II: infrared, III: x-rays, IV: radio waves
- BI: blue light, II: red light, III: orange light, IV: green light
- CI: x-rays, II: blue light, III: infrared, IV: microwaves
- DI: gamma waves, II: microwaves, III: infrared, IV: visible light
16.Sound waves can be propagated through fluids and solids. Which statements are correct? I. Sound waves have constant speed in air II. Thunder always arrives before lightning because of the difference in wave speeds. III. Sound waves can be modelled using the equation v = fλ IV. Vibrations from an earthquake will be felt in the ground before they are heard, because of the difference in wave speeds
Hard
- AI and IV
- BII and IV
- CI, III and IV
- DIII and IV
17.Which cannot be observed with ultrasound?
Medium
- Adiffraction
- Bdispersion
- Cpolarisation
- Drefraction
18.The diagram shows a cross-sectional view through a water wave travelling from left to right. At which point is the water moving with maximum speed in the upward direction?
Hard
- AAt a crest
- BAt a trough
- CAt the equilibrium position moving upwards
- DAt the equilibrium position moving downwards
19.The diagram shows a wave with a frequency of 25 Hz travelling from left to right. At this instant, the displacement of point X is zero. What is the shortest time to elapse for the displacement of point Y to be zero?
Hard
- A0.005 s
- B0.01 s
- C0.05 s
- D0.10 s
20.The graphs below show the displacement of a wave as a function of time and position. What is a correct expression for wave speed?
Hard
- A2P/Q
- B3P/Q
- C2Q/P
- D3Q/P
21.The star Deneb emits EM waves of wavelengths 50 000 μm, 500 μm, 0.5 μm and 0.005 μm. Which row correctly identifies the areas of the EM spectrum to which these wavelengths belong?
Challenge
- AMicrowave, Infrared, Visible, X-ray
- BRadio, Microwave, Infrared, Visible
- CInfrared, Visible, Ultraviolet, X-ray
- DMicrowave, Infrared, Ultraviolet, Gamma
22.Visible light has wavelengths ranging from 400 nm to 700 nm. What is the maximum frequency of visible light?
Challenge
- A3 × 10⁻¹⁸ Hz
- B7.5 × 10⁻¹⁸ Hz
- C3 × 10¹⁶ Hz
- D7.5 × 10¹⁴ Hz
23.The diagram shows the positions of three points on a string as a transverse wave travels along it from left to right. Which row correctly shows the velocities of the points on the string?
Challenge
- A1: ↓, 2: ↓, 3: ↓
- B1: ↑, 2: ↑, 3: ↓
- C1: ↑, 2: ↓, 3: ↑
- D1: ↓, 2: ↑, 3: ↓
24.The diagram shows a water particle on the crest of a wave in a ripple tank. Which arrow correctly shows the force acting on the particle?
Challenge
- AArrow pointing upwards
- BArrow pointing downwards
- CArrow pointing left
- DArrow pointing right
25.Electromagnetic waves can travel through a vacuum.
Easy
True or false?
26.Sound waves travel faster in gases than in solids.
Easy
True or false?
27.The frequency of a wave is directly proportional to its wavelength when wave speed is constant.
Medium
True or false?
28.The pitch of a sound is determined by its frequency.
Easy
True or false?
29.All electromagnetic waves travel at the same speed in a vacuum.
Medium
True or false?
30.Which of the following are properties of travelling waves? (select all that apply)
Medium
- AThey transfer energy
- BThey transfer matter
- CThey are generated by oscillating sources
- DThey can propagate in a vacuum regardless of type
- EThey travel away from the source
31.Which of the following statements about electromagnetic waves are correct? (select all that apply)
Hard
- AThey are longitudinal waves
- BThey are generated by oscillating electric and magnetic fields
- CThey can travel through a vacuum
- DThey all have the same frequency
- EThey travel at the speed of light in a vacuum
32.Match each wave type to its correct description.
Medium
- Transverse wave
- Longitudinal wave
- Electromagnetic wave
- Sound wave
- Oscillations parallel to direction of energy transfer
- Can travel through a vacuum
- Oscillations perpendicular to direction of energy transfer
- Requires a medium and is longitudinal
33.Arrange the following regions of the electromagnetic spectrum in order of increasing frequency.
Medium
- Radio waves
- Infrared
- Visible light
- Ultraviolet
- X-rays
34.Arrange the following regions of the electromagnetic spectrum in order of increasing wavelength.
Hard
- Gamma rays
- X-rays
- Ultraviolet
- Visible light
- Infrared
- Microwaves
35.Which statement correctly describes the relationship between frequency and wavelength for a wave of constant speed?
Medium
- AAs wavelength increases, frequency increases
- BAs wavelength increases, frequency decreases
- CFrequency is independent of wavelength
- DFrequency is directly proportional to wavelength
36.Which of the following is a correct unit for wave speed?
Medium
- Am s⁻²
- Bm s⁻¹
- CHz
- Dm
37.A wave has a frequency of 500 Hz and a wavelength of 0.68 m. What is its speed?
Hard
- A340 m/s
- B735 m/s
- C0.00136 m/s
- D500 m/s
38.Which of the following statements about sound waves is correct?
Hard
- ASound waves are transverse and can travel through a vacuum
- BSound waves are longitudinal and travel faster in solids than in gases
- CSound waves are electromagnetic and travel at the speed of light
- DSound waves have a constant speed of 340 m/s regardless of temperature
39.A wave has a period of 0.005 s and a wavelength of 0.34 m. What is its speed?
Challenge
- A68 m/s
- B0.0017 m/s
- C1700 m/s
- D340 m/s
40.Match each wave property to its correct definition.
Easy
- Wavelength
- Amplitude
- Period
- Frequency
- Length of one complete oscillation measured from the same point on two consecutive waves
- Maximum displacement of an oscillating wave from its equilibrium position
- Time taken for a complete oscillation to pass a fixed point
- Number of complete oscillations to pass a fixed point per second
41.Calculate the frequency of an infrared wave with wavelength λ = 3.0 × 10⁻⁶ m. Give your answer in Hz.
Medium
42.A wave has a period of 0.02 s. Calculate its frequency in Hz.
Medium
43.A sound wave travels at 340 m/s with a frequency of 170 Hz. Calculate its wavelength in metres.
Medium
44.Complete the sentence about wave types.
Easy
A ____ wave has oscillations perpendicular to the direction of energy transfer, while a ____ wave has oscillations parallel to the direction of energy transfer.
45.Complete the sentence about sound waves.
Easy
Sound waves are ____ waves and require a ____ to propagate.
46.Name the two regions of a longitudinal wave where particles are closer together and further apart.
Medium
The region where particles are closer together is called a ____, and the region where they are further apart is called a ____.
47.What term describes the maximum displacement of a wave from its equilibrium position?
Easy
48.What is the name for the time taken for one complete oscillation to pass a fixed point?
Medium
49.What is the name of the region in a longitudinal wave where particles are furthest apart?
Medium
50.A wave has a frequency of 250 Hz and a wavelength of 1.2 m. Calculate its speed in m/s.
Medium
51.An electromagnetic wave has a wavelength of 2.0 × 10⁻⁷ m. Calculate its frequency in Hz. Use c = 3.0 × 10⁸ m/s.
Medium
52.What is the name of the region in a longitudinal wave where particles are closest together?
Medium
53.Outline one difference between a mechanical wave and an electromagnetic wave.
Medium
54.Describe, in terms of displacement, the motion of particles in a longitudinal wave.
Medium
55.Outline what is meant by the speed of a wave.
Easy
56.Calculate the frequency of an infrared wave with wavelength λ = 3.0 × 10⁻⁶ m. Give your answer in Hz.
Medium
- A110000000000000 Hz
- B90000000000000 Hz
- C100000000000000 Hz
- D120000000000000 Hz
57.A wave has a period of 0.02 s. Calculate its frequency in Hz.
Medium
- A60 Hz
- B55 Hz
- C50 Hz
- D45 Hz
58.A sound wave travels at 340 m/s with a frequency of 170 Hz. Calculate its wavelength in metres.
Medium
- A2 m
- B3 m
- C4 m
- D1 m
59.A wave has a frequency of 250 Hz and a wavelength of 1.2 m. Calculate its speed in m/s.
Medium
- A360 m/s
- B300 m/s
- C270 m/s
- D330 m/s
60.An electromagnetic wave has a wavelength of 2.0 × 10⁻⁷ m. Calculate its frequency in Hz. Use c = 3.0 × 10⁸ m/s.
Medium
- A1500000000000000 Hz
- B1800000000000000 Hz
- C1650000000000000 Hz
- D1350000000000000 Hz

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