Ch 1 · 7 Waves · A Level Physics 9702
Topic 1 of 2 in Waves and Superposition — A Level Physics 9702 — 89 lessons.
Introduction
Waves carry energy and information, from sound and light to the radio signals of a phone. This topic builds the language for describing any wave, then looks at two special effects: the Doppler shift and polarisation. (Syllabus topic 7: sections 7.1–7.5.)
Key ideas — 7.1 (a) Wave motion and the terms
A progressive wave transfers energy from one place to another without transferring matter; the particles of the medium oscillate about fixed positions. Wave motion can be seen on a rope, along a slinky spring and in a ripple tank.
🧑🏫 Teacher's explanation
Imagine a long rope tied to a wall. If you shake one end up and down, you see a wave traveling toward the wall. Notice that the rope itself doesn't travel to the wall; only the 'wiggle' (the energy) moves. The rope particles just move up and down around their original spot. This is the essence of a progressive wave: energy moves, but matter stays put.
📖 Definitions
🔍 Worked example — Easy
A water wave in a ripple tank has a frequency of 5.0 Hz and a wavelength of 0.20 m. Calculate the speed of the wave.
🔍 Worked example — Standard
A wave has a period of 0.025 s. Calculate its frequency.
🔍 Worked example — Exam-style
A progressive wave has a speed of 340 m s^-1 and a frequency of 680 Hz. Calculate the wavelength and determine the phase difference between two points separated by 0.001 m.
⚠️ Common errors
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🎯 Exam question
Key ideas — 7.1 (b) Using a cathode-ray oscilloscope (CRO)
A CRO displays a graph of p.d. (from a microphone, say) against time.
🧑🏫 Teacher's explanation
Imagine a Cathode-Ray Oscilloscope (CRO) as a high-speed camera that doesn't take pictures, but instead draws a continuous line of light on a screen. Instead of a single snapshot, it traces the movement of electrons. If you plug a microphone into it, the CRO draws the electrical signal from the microphone. As the sound wave vibrates, the voltage changes, and the electron beam moves up and down, creating a wave pattern on the screen.\n\nTo understand the CRO, think of it like a graph paper that is constantly moving. The horizontal axis (x-axis) represents time, and the vertical axis (y-axis) represents voltage. The 'Time-base' setting tells you how much time passes for every square (division) you move horizontally. The 'Y-gain' setting tells you how much voltage changes for every square you move vertically. By looking at the grid, you can translate the visual 'size' of the wave into real physical values like frequency and amplitude.
📖 Definitions
🔍 Worked example — Easy
A signal on a CRO shows 4 full cycles across 20 horizontal divisions. The time-base is set to 5.0 ms/div. Calculate the frequency f of the signal.
🔍 Worked example — Standard
A waveform on a CRO has a peak-to-peak displacement of 6 divisions. The Y-gain is set to 2.5 V/div. Calculate the amplitude A of the wave.
🔍 Worked example — Exam-style
A signal has a frequency of 500 Hz. On the CRO screen, one complete cycle occupies 8 divisions. Determine the required time-base setting in ms/div.
⚠️ Common errors
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🎯 Exam question
Key ideas — 7.1 (c) The wave equation
Derivation. In one period T, the wave travels one wavelength λ:
🧑🏫 Teacher's explanation
Imagine you are standing by a lake and you drop a stone. You see a circular ripple move outward. If you time how long it takes for one full wave crest to pass a specific leaf in the water, that is the period T. If you measure the distance between two consecutive crests, that is the wavelength λ. The speed v at which that ripple travels is simply how far one wavelength travels in one period.
📖 Definitions
🔍 Worked example — Easy
A water wave has a frequency of 5.0 Hz and a wavelength of 0.20 m. Calculate the speed of the wave.
🔍 Worked example — Standard
A sound wave travels at 340 m s^-1 with a frequency of 680 Hz. Calculate its wavelength.
🔍 Worked example — Exam-style
An electromagnetic wave has a wavelength of 6.0 × 10^-7 m. Calculate the frequency of this wave, assuming it travels at the speed of light c = 3.0 × 10^8 m s^-1.
⚠️ Common errors
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🎯 Exam question
Key ideas — 7.1 (d) Energy and intensity
A progressive wave transfers energy. Intensity is the power per unit area, measured at right angles to the direction of travel:
🧑🏫 Teacher's explanation
Think about a wave in the ocean. A single wave carries energy from the deep ocean toward the shore. If you stand in the water, the 'intensity' of that wave is how much energy hits you per second through a specific area of your body. If the wave gets much taller (larger amplitude), it doesn't just hit you twice as hard; it hits you much more forcefully because the energy is tied to the square of that height.
📖 Definitions
🔍 Worked example — Easy
A progressive wave has a power of 20 W and is spread over an area of 5 m^2. Calculate the intensity.
🔍 Worked example — Standard
The amplitude of a water wave is increased from 2.0 cm to 6.0 cm. Calculate the factor by which the intensity increases.
🔍 Worked example — Exam-style
A point source radiates waves uniformly in all directions. At a distance of 2.0 m, the intensity is 10 W m^-2. Calculate the intensity at a distance of 5.0 m.
⚠️ Common errors
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🎯 Exam question
Key ideas — 7.2 Transverse and longitudinal waves
Graphs. A displacement–distance graph is a snapshot of the wave at one instant; you can read the wavelength and amplitude. A displacement–time graph shows how one point oscillates; you can read the period and amplitude.
🧑🏫 Teacher's explanation
Imagine you are standing in a large crowd at a stadium. If everyone performs 'the wave' by standing up and sitting down in sequence, the disturbance moves around the stadium, but the people themselves only move up and down. This is a transverse wave: the oscillation is perpendicular to the direction of energy travel. Now, imagine you are at the front of that same crowd and you give a single person a gentle shove. That person bumps the person in front, who bumps the next, creating a 'pulse' that travels through the crowd. The people are moving forward and backward, parallel to the direction the pulse travels. This is a longitudinal wave.
📖 Definitions
🔍 Worked example — Easy
A transverse water wave has a wavelength of 0.50 m and a frequency of 2.0 Hz. Calculate the speed of the wave.
🔍 Worked example — Standard
A sound wave (longitudinal) has a frequency of 680 Hz. The speed of sound in air is 340 m s^-1. Calculate the wavelength.
🔍 Worked example — Exam-style
A plane-polarised light beam of intensity I_0 = 100 W m^-2 is incident on a second polarising filter (the analyzer) oriented at an angle of 60^° to the transmission axis of the first filter. Calculate the intensity of the transmitted light.
⚠️ Common errors
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🎯 Exam question
Key ideas — 7.3 Doppler effect for sound
When a source of sound moves relative to a stationary observer, the observed frequency differs from the frequency emitted.
🧑🏫 Teacher's explanation
Imagine you are standing on a sidewalk and an ambulance with a siren is driving past you. As it approaches, the sound seems high-pitched, but as it passes and moves away, the pitch suddenly drops. This change in pitch is due to the Doppler effect.
📖 Definitions
🔍 Worked example — Easy
A car horn emits a sound at a frequency of 400 Hz. The car is traveling towards a stationary observer at 20.0 m s^-1. Calculate the observed frequency. (Speed of sound in air is 340 m s^-1)
🔍 Worked example — Standard
An ambulance siren emits a sound at 720 Hz. The ambulance is moving away from a stationary observer at 30.0 m s^-1. Calculate the observed frequency. (Speed of sound is 340 m s^-1)
🔍 Worked example — Exam-style
A source of sound moves at v_s towards a stationary observer. The source frequency is f_s. If the observed frequency f_o is exactly double the source frequency (f_o = 2f_s), find the speed of the source v_s in terms of the speed of sound v.
⚠️ Common errors
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🎯 Exam question
Key ideas — 7.4 The electromagnetic spectrum
All electromagnetic waves are transverse and travel at the same speed c in free space, 3.00 × 10^8 m s⁻¹.
🧑🏫 Teacher's explanation
Imagine you are standing on a pier watching ripples on a lake. Even if the ripples are different sizes (wavelengths) or moving at different speeds (frequencies), they all travel across the water at the same speed determined by the water's depth. Electromagnetic (EM) waves are similar, but they don't need water; they travel through the vacuum of space at a constant speed c = 3.00 × 10^8 m s^-1.
📖 Definitions
🔍 Worked example — Easy
State the wavelength range of visible light in free space.
🔍 Worked example — Standard
A plane-polarised light wave with intensity I_0 = 1.20 × 10^-2 W m^-2 is incident on a polarising filter. Calculate the intensity I transmitted if the plane of polarisation is at an angle of θ = 30^° to the transmission axis of the filter.
🔍 Worked example — Exam-style
A plane-polarised light wave of intensity I_0 = 0.500 W m^-2 is incident on a second polarising filter. The angle between the plane of polarisation of the light and the transmission axis of the filter is 60^°. Calculate the transmitted intensity.
⚠️ Common errors
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🎯 Exam question
Key ideas — 7.5 Polarisation
Polarisation is a phenomenon of transverse waves only. In an unpolarised wave (e.g. light from a lamp), the oscillations occur in many planes perpendicular to the direction of travel. A plane-polarised wave oscillates in one plane only. Longitudinal waves (sound) cannot be polarised, because their oscillations are already along the direction of travel.
🧑🏫 Teacher's explanation
Imagine you are holding a long rope tied to a wall. If you shake the rope up and down, you create a transverse wave where the rope moves vertically. If you shake it side-to-side, the rope moves horizontally. In 'unpolarised' light, like light from a bulb, the electric field is shaking in every possible direction perpendicular to the path of the wave.
📖 Definitions
🔍 Worked example — Easy
A beam of plane-polarised light with intensity I_0 = 12.0 W m^-2 is incident on a polarising filter. The transmission axis of the filter is at an angle of θ = 60.0^° to the plane of polarisation. Calculate the intensity of the transmitted light.
🔍 Worked example — Standard
Two polarising filters are placed one after the other. The first filter is oriented vertically. The second filter is oriented at an angle of 30.0^° to the first. If the intensity of the light after the first filter is 0.800 W m^-2, find the intensity of the light after the second filter.
🔍 Worked example — Exam-style
A beam of plane-polarised light passes through two polarising filters. The first filter is at 0^° and the second is at 45.0^°. The third filter is at 90.0^° relative to the first. If the initial intensity of the plane-polarised light entering the first filter is 4.00 W m^-2, calculate the final intensity after the third filter.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
(a) State the equation used to calculate the transmitted intensity I. [1] (b) The beam passes through a second polarising filter which is oriented at an angle of 60.0^° to the first filter. If the intensity after the first filter is 2.00 W m^-2, calculate the intensity of the light after it has passed through the second filter. [2] [3 marks]
Practical notes
Worked example
Example 1: CRO. One cycle spans 4.0 divisions at a time-base of 0.50 ms/div; the trace is 2.5 divisions from centre to peak at 0.20 V/div. Period = 2.0 ms, so f = 500 Hz; amplitude = 0.50 V.
🔍 Worked example — Easy
A signal on a CRO shows one complete cycle spanning 4.0 divisions. The time-base is set to 0.50 ms/div and the vertical scale (y-gain) is 0.20 V/div. Calculate the frequency and the peak voltage amplitude.
🔍 Worked example — Exam-style
An ambulance siren emits sound at a frequency of 700 Hz. The ambulance is traveling towards a stationary observer at 30 m s^-1. The speed of sound in air is 340 m s^-1. Calculate the observed frequency f_o.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) In one period T the wave moves one wavelength: v = λ/T = fλ. (2) 0.15/0.60 = tfrac14 cycle = 90° (π/2 rad). (3) It falls to one quarter. (4) 400 × 340/(340 + 25) = 373 Hz. (5) 400 nm to 700 nm. (6) cos^2 30° = 0.75.