Ch 1 · 3.1 General Properties of Waves · O Level Physics 5054
Topic 1 of 7 in Waves — O Level Physics 5054 — 60 lessons.
Introduction
Drop a stone into a pond and ripples spread out to the edge, but the water itself just bobs up and down. A leaf floating on the surface is not carried to the shore. What travels outward is energy. Light, sound, radio signals and earthquakes all move energy this way, as waves. (Syllabus section 3.1.)
Key ideas — Waves transfer energy, not matter
A wave carries energy from one place to another without transferring matter. The particles of the material (the medium) only vibrate about their usual positions; they do not travel with the wave.
🧑🏫 Teacher's explanation
Imagine you are standing in a crowded stadium and start a 'Mexican Wave'. You stand up and sit down, and the 'wave' moves around the stadium. However, you haven't actually moved from your seat; you only moved up and down. The energy (the visual wave) traveled around the crowd, but the people (the matter) stayed in their original positions.
📖 Definitions
🔍 Worked example — Easy
A transverse wave on a rope has a wavelength of 0.5 m and a frequency of 10 Hz. Calculate the wave speed v.
🔍 Worked example — Standard
A longitudinal sound wave has a frequency of 440 Hz and a speed of 340 m/s. Calculate its wavelength λ.
🔍 Worked example — Exam-style
A student observes a wave on a string. The distance between two consecutive crests is 0.20 m. The frequency of the wave is 50 Hz. Calculate the speed of the wave and state if the vibration is parallel or perpendicular to the direction of travel if it is a transverse wave.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Key ideas — Describing a wave
🧑🏫 Teacher's explanation
Imagine a stadium full of people performing 'the wave'. Each person stands up and sits down (vibrates), but the people themselves don't move from their seats; only the 'wave' of movement travels around the stadium. This is the fundamental nature of a wave: it transfers energy from one place to another without moving matter from one place to another.
📖 Definitions
🔍 Worked example — Easy
A water wave has a frequency of 5 Hz and a wavelength of 0.2 m. Calculate the wave speed v.
🔍 Worked example — Standard
A sound wave travels at 340 m/s with a frequency of 680 Hz. Calculate its wavelength λ.
🔍 Worked example — Exam-style
A student observes a wave on a string. The distance between a crest and the next trough is 0.15 m. If the frequency is 10 Hz, calculate the wave speed v.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Key ideas — The wave equation
v = fλ
🧑🏫 Teacher's explanation
Imagine you are standing on a pier watching waves come into a harbor. If you see 2 waves pass you every second, and each wave is 3 meters long from crest to crest, you can easily figure out how fast the wave train is moving. You just multiply them: 2 waves/sec × 3 m/wave = 6 meters per second.
📖 Definitions
🔍 Worked example — Easy
A water wave has a frequency of 5 Hz and a wavelength of 0.2 m. Calculate the speed of the wave.
🔍 Worked example — Standard
A sound wave travels at 340 m/s with a frequency of 680 Hz. Calculate its wavelength.
🔍 Worked example — Exam-style
An ocean wave is observed to have a wavelength of 4.0 m. If the wave speed is 8.0 m/s, calculate the frequency of the wave.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Key ideas — Transverse and longitudinal waves
Transverse wave: the vibrations are at right angles to the direction the energy travels.
🧑🏫 Teacher's explanation
Imagine you are standing in a crowded stadium performing 'the wave'. You stand up and sit down (vibration), but you don't move from your seat (no matter transfer). The 'wave' travels around the stadium (energy transfer). This is exactly how waves work: they move energy from point A to point B without moving the actual particles from A to B.
📖 Definitions
🔍 Worked example — Easy
A water wave has a frequency of 5.0 Hz and a wavelength of 0.20 m. Calculate the wave speed v.
🔍 Worked example — Standard
A sound wave (longitudinal) travels at 340 m/s with a frequency of 680 Hz. Calculate its wavelength λ.
🔍 Worked example — Exam-style
An earthquake produces a P-wave (longitudinal) traveling at 6000 m/s and an S-wave (transverse) traveling at 3500 m/s. If the frequency of the P-wave is 2.0 Hz, calculate the wavelength of the S-wave.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Key ideas — Reflection, refraction and diffraction
Reflection at a plane surface. When waves hit a flat barrier, they bounce back. The angle at which they hit equals the angle at which they leave. The wavelength, frequency and speed do not change.
🧑🏫 Teacher's explanation
Imagine you are standing at the edge of a swimming pool. If you drop a stone, the ripples (waves) carry the energy from the splash to the wall. Notice that the water molecules themselves don't travel to the wall; they just bob up and down. This is the core concept: waves move energy, not matter.
📖 Definitions
🔍 Worked example — Easy
A water wave has a frequency of 5 Hz and a wavelength of 0.4 m. Calculate the wave speed v.
🔍 Worked example — Standard
A wave travels from deep water into shallow water. In deep water, the speed is 2.0 m/s and the wavelength is 0.5 m. In shallow water, the speed is 1.5 m/s. Calculate the wavelength in shallow water.
🔍 Worked example — Exam-style
A sound wave with a frequency of 500 Hz passes through a gap. If the wave speed in air is 340 m/s, calculate the wavelength. If the gap size is 0.5 m, describe the diffraction effect.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Practical notes
The ripple tank. A shallow glass-bottomed tank of water, with a light above it so that the waves cast bright and dark lines (wavefronts) on a screen below. A vibrating bar (a dipper driven by a motor) makes straight plane waves.
Worked example
Example 1. A water wave has frequency 5.0 Hz and wavelength 0.040 m. Find its speed.
🔍 Worked example — Easy
A water wave has frequency f = 5.0 Hz and wavelength λ = 0.040 m. Calculate the wave speed v.
🔍 Worked example — Standard
A radio station broadcasts at f = 100 MHz. Radio waves travel at v = 3.0 × 10^8 m/s. Find the wavelength λ.
🔍 Worked example — Exam-style
Ten crests pass a post in 4.0 s, and the distance between neighbouring crests is 1.2 m. Find the frequency f and the wave speed v.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) Energy is transferred; matter is not. (2) (a) the distance between two consecutive identical points, e.g. two consecutive crests; (b) the number of wavelengths passing a point per unit time; (c) the maximum distance from the mean position. (3) Transverse: light (any EM wave), water surface waves, S-waves. Longitudinal: sound, P-waves. (4) v = 680 × 0.50 = 340\ m/s. (5) Speed decreases, wavelength decreases, frequency stays the same. (6) Sound's wavelength is similar to the width of a doorway, so it diffracts a lot; light's wavelength is far smaller than the doorway, so it diffracts very little.