Wave Investigations
In 1738, French Académie des Sciences measured sound speed at 332 m/s using cannon fire and two stopwatches, 2.7% accurate by modern standards.
● Know
- That wave speed depends on the medium the wave travels through
- The difference between reflection and refraction
- How to process and represent wave data in tables and graphs
● Understand
- Why sound travels faster through solids and liquids than through gases
- How to identify trends and patterns in experimental data
- That conclusions must be supported by evidence from the investigation
● Can do
- Design a fair test to investigate wave properties
- Measure wave speed using appropriate tools and units
- Draw evidence-based conclusions from wave investigation data
Stand 100 m from a solid brick wall and clap two blocks of wood together sharply: you will hear a faint echo roughly 0.6 seconds later as the sound travels to the wall and back. Time that echo accurately and you have measured the speed of sound, the same method French scientists used with cannon fire in 1738 to get 332 m/s, within 2.7% of today's accepted 343 m/s. Measuring the speed of sound is a classic physics experiment that applies the wave equation $v = d/t$, but the precision of your result depends entirely on controlling sources of error.
Echo method: Stand a known distance from a reflecting surface. Make a sharp sound and measure the time until you hear the echo. The sound travels to the wall and back, so total distance = 2d. Speed = 2d/t.
Two-station method: Two people stand a known distance apart. One makes a sound while simultaneously sending a visual signal (waving a flag or turning on a light). The second person starts timing on seeing the visual signal and stops on hearing the sound. The visual signal travels essentially instantaneously (at light speed), so the measured time is just the sound travel time.
Sources of error: Reaction time in starting/stopping the stopwatch, inaccurate distance measurement, wind affecting sound speed, temperature variations, and echoes from multiple surfaces.
Using the echo method: stand 50 metres from a building. Clap your hands sharply. The echo returns after 0.29 seconds. Speed = 2 × 50 / 0.29 = 345 m/s. This is close to the expected value of 343 m/s at 20C. The small difference could be due to temperature (slightly warmer air speeds up sound), measurement error in distance, or reaction time. To improve accuracy, take multiple measurements and calculate a mean. Use a larger distance to reduce the percentage error from reaction time (human reaction time is about 0.2 s, which is a large fraction of 0.29 s but a smaller fraction of longer travel times).
Australian acoustic standards: The National Measurement Institute calibrates instruments for measuring sound speed and other acoustic properties. Precise knowledge of sound speed is essential for sonar, medical ultrasound, and non-destructive testing of materials. Australian researchers at the CSIRO develop acoustic techniques for measuring ocean temperature (since sound speed in water depends on temperature, salinity, and pressure), providing large-scale monitoring of ocean warming without deploying thousands of thermometers.
The speed of sound depends on how loud the sound is. This is false. Sound speed in a given medium depends only on the medium properties (temperature, density, elasticity), not on amplitude or frequency. A whisper and a shout travel at the same speed in air. A high-pitched whistle and a low-pitched drum travel at the same speed. This is why a distant orchestra sounds coherent - all frequencies arrive together. If different frequencies travelled at different speeds, music would become distorted with distance, with high notes arriving before low notes.
Put these steps for measuring the speed of sound into the correct order.
- Start timing when you see the sound being made.
- Record the time for the sound to travel to the wall and back.
- Calculate speed = 2 × distance / time.
- Stop timing when you hear the echo return.
- Stand a known distance from a large flat wall.
- Make a sharp sound (clap or hammer strike).
Standing waves (or stationary waves) form when two waves of the same frequency and amplitude travel in opposite directions and superpose. Unlike travelling waves, standing waves do not transfer energy from place to place - the energy oscillates between kinetic and potential forms at fixed locations.
Nodes: Points where destructive interference produces zero amplitude. The medium does not move at nodes. Spacing between adjacent nodes = λ/2.
Antinodes: Points where constructive interference produces maximum amplitude. Spacing between adjacent antinodes = λ/2. Nodes and antinodes alternate, spaced λ/4 apart.
Musical instruments: Standing waves on strings (guitars, violins) and in air columns (flutes, trumpets) produce musical notes. The fundamental frequency corresponds to a standing wave with nodes at the fixed ends and an antinode in the middle. Higher harmonics have additional nodes.
A guitar string of length 0.65 m vibrates at its fundamental frequency. The wavelength is twice the string length: λ = 2L = 1.30 m. If the string tension and mass give a wave speed of 260 m/s, the fundamental frequency is f = v/λ = 260/1.30 = 200 Hz. When you fret the string at the 12th fret (halfway), the vibrating length becomes 0.325 m, the wavelength becomes 0.65 m, and the frequency doubles to 400 Hz - one octave higher. This is why halving the vibrating length doubles the frequency, a fundamental principle of all string instruments.
Australian musical acoustics: The University of New South Wales has an internationally renowned music acoustics research group. They study the physics of Australian instruments, including the didgeridoo - a wind instrument that produces complex standing wave patterns with strong drone frequencies and formant regions that create its characteristic timbre. Didgeridoo playing requires circular breathing and precise vocal tract shaping to amplify specific harmonics. Australian researchers use acoustic analysis to understand how traditional instruments produce their distinctive sounds and how craft traditions encode acoustic knowledge.
Standing waves and stationary waves are different things. This is false. They are the same phenomenon with two names. Standing wave emphasises that the wave pattern does not travel; stationary wave emphasises that the nodes and antinodes remain in fixed positions. Both terms describe waves formed by superposition of oppositely travelling waves with no net energy transport. Some textbooks prefer one term; others use both interchangeably. Do not be confused by the dual terminology.
Find the error in this student explanation of standing waves.
- Standing waves are formed by two waves travelling in opposite directions.
- In a standing wave, nodes remain stationary while antinodes oscillate.
- Energy does not travel in a standing wave; it is stored in the oscillating medium.
- The student is correct because all waves transfer energy.
Resonance occurs when a system is driven at its natural frequency of oscillation. At resonance, energy transfer is maximised and oscillation amplitude grows dramatically.
Beneficial resonance:
- Musical instruments: The body of a guitar or violin resonates at certain frequencies, amplifying the string vibrations.
- Radio/TV tuning: The receiver circuit is tuned to resonate at the broadcast frequency, selectively amplifying that signal.
- Microwave ovens: The microwave frequency (2.45 GHz) is chosen to resonate with water molecules, maximising energy absorption.
- MRI: Nuclear magnetic resonance aligns hydrogen nuclei with radio waves at their resonant frequency in a magnetic field.
Destructive resonance:
- Bridge collapses: The Tacoma Narrows Bridge (1940) collapsed when wind vortices matched the bridge torsional natural frequency.
- Machine vibration: Rotating machinery can vibrate destructively if operating speed matches a natural frequency.
A child on a swing demonstrates resonance intuitively. Pushing randomly does little. Pushing at exactly the right moment - once per swing cycle, at the natural frequency - makes the swing go higher and higher with minimal effort. This is because each push adds energy in phase with the existing motion. If you push at the wrong frequency (twice per cycle, for example), some pushes oppose the motion and cancel out the energy transfer. Resonance is about timing - matching the driving frequency to the system natural frequency.
Australian resonance engineering: Engineers designing the Sydney Harbour Bridge and other major structures carefully model natural frequencies to avoid resonance with wind, traffic, and pedestrian loads. The Millennium Bridge in London famously wobbled when pedestrian walking frequencies matched a lateral mode - Australian bridge engineers learned from this and now incorporate damping systems to prevent similar problems. The ANU Department of Engineering studies vibration and acoustics, including active noise cancellation and vibration damping technologies used in Australian mining and transport equipment.
Resonance creates energy from nothing. This is false. Resonance does not violate conservation of energy. It simply transfers energy from the driving source to the oscillating system very efficiently. The amplitude grows until energy dissipation (friction, radiation, damping) equals the energy input per cycle. At that point, a steady state is reached. Without a continuous energy source, resonant oscillations decay. The Tacoma Narrows Bridge collapsed because wind energy input exceeded the bridge capacity to dissipate it, not because resonance created energy.
Find the error in this statement about resonance.
- Resonance can cause bridges to collapse if wind matches the natural frequency.
- Resonance is used deliberately in musical instruments to amplify sound.
- Microwave ovens use resonance to make water molecules vibrate.
- MRI machines use nuclear magnetic resonance for imaging.
- Resonance is dangerous in some situations but useful in others.
Wrong: "Reflection and refraction are the same thing." No � reflection is when a wave bounces back from a surface; refraction is when a wave bends as it passes from one medium into another.
Right: Reflection and refraction are distinct wave behaviours. Reflection occurs when a wave bounces back from a boundary, obeying the law that the angle of incidence equals the angle of reflection. Refraction occurs when a wave crosses into a different medium and changes speed, causing it to change direction. Both can happen at the same boundary, but they are separate processes.
Wrong: "Sound travels at the same speed everywhere." No � sound speed depends on the medium and its temperature. Sound travels about four times faster through water than through air.
Right: Sound speed varies with the medium and its conditions. In air at 20°C, sound travels at roughly 340 m/s; in water it travels at about 1480 m/s; in steel it can exceed 5000 m/s. Temperature also matters, warmer air molecules move faster, so sound travels faster in hot air than in cold. There is no single universal "speed of sound."
Wrong: "A conclusion should always prove the hypothesis correct." No � a valid conclusion reports what the data actually shows, even if it contradicts the original prediction. Unexpected results can be just as scientifically valuable.
Right: A valid scientific conclusion must honestly reflect what the data shows, even if it contradicts the hypothesis. Reporting results accurately is fundamental to scientific integrity. A hypothesis that is not supported by evidence is still valuable: it narrows down possibilities, prompts new questions and drives better experimental design.
Waves in Australian Research and Life
Great Barrier Reef monitoring: Marine scientists use sound waves (sonar) and light waves (satellite imaging) to monitor coral health. Sound travels quickly through seawater, allowing researchers to map the reef floor, while light-based sensors measure water clarity and temperature from above.
Australian surf forecasting: Agencies like the Bureau of Meteorology use wave data from buoys and satellites to predict surf conditions. Understanding how water waves refract as they approach different coastlines helps predict where waves will break and how large they will be.
Indigenous knowledge of seismic signals: Aboriginal and Torres Strait Islander Peoples have traditionally read signs from the land, including vibrations and tremors. This knowledge reflects a sophisticated understanding that energy transfers through the earth and can signal events at a distance, a concept central to modern wave investigations.
✍ Copy Into Your Books
▾Wave Speed in Different Media
- Wave speed depends on the medium
- Solids > liquids > gases for sound
- v = distance / time or v = f × λ
Reflection and Refraction
- Reflection: wave bounces back from a surface
- Refraction: wave bends when changing medium
- Both are caused by waves meeting boundaries
Processing and Concluding
- Organise data in tables with units
- Calculate means and plot graphs
- Conclusions must be evidence-based
Design a Wave Speed Investigation
Analyse Wave Data
| Material | Speed of sound (m/s) | Density |
|---|---|---|
| Air | 343 | Low |
| Water | 1 480 | Medium |
| Steel | 5 960 | High |
At the start of this lesson you were shown a CSIRO researcher who scrapped two years of data because a single uncontrolled variable, the angle of a sensor, had gone unnoticed, and how that one oversight turned a potential discovery into a mistake.
Now that you've worked through the lesson, how has your thinking shifted? Can you explain that hook idea more precisely using what you've learned today?
Q1. 1. Explain why sound travels faster through steel than through air. Refer to particle arrangement in your answer. 4 MARKS
Q2. 2. A light ray strikes a mirror at an angle of 30° to the normal. Describe what happens to the ray, naming the phenomenon and stating the angle of reflection. Explain why a straw in a glass of water appears bent. 4 MARKS
Q3. 3. A student conducts an investigation into wave speed in different materials and obtains the following results: air 330 m/s, water 1 450 m/s, glass 4 800 m/s. Explain how the student should process this data and what evidence-based conclusion they should draw. 4 MARKS
Revisit Your Thinking
Go back to your Think First answer. Has your understanding changed?
- Can you now explain why you see a splash before you hear the sound?
- How would you improve your experimental design for measuring sound speed in different media?
Model answers (click to reveal)
Answers
▾MCQ 1
CSound travels fastest through steel because the particles in a solid are tightly packed, allowing vibrations to pass quickly from one particle to the next.
MCQ 2
BWhen light passes from air into water, it slows down and bends toward the normal line. This bending is called refraction.
MCQ 3
AThe sound travels to the cliff and back in 2 seconds, so the one-way time is 1 second. Distance = speed x time = 343 x 1 = 343 m.
MCQ 4
DTo test how depth affects wave speed, the student must keep all other variables constant, including frequency. Changing frequency would make it impossible to tell whether depth or frequency caused any observed change.
MCQ 5
BThe most likely explanations are that the air temperature was lower than 20 °C (sound speed decreases with temperature) or that there were measurement errors in timing or distance. Both are scientifically valid sources of discrepancy.
Short Answer 1
Model answer: Sound travels faster through steel than air because steel is a solid with particles packed closely together in a fixed pattern. When one particle vibrates, it quickly passes the vibration to neighbouring particles. In air, particles are far apart and move randomly, so it takes longer for the disturbance to travel from particle to particle. The closer packing in solids allows more efficient energy transfer, resulting in a higher wave speed.
Short Answer 2
Model answer: When a light ray strikes a mirror at 30° to the normal, it reflects off the surface at 30° to the normal (law of reflection). This phenomenon is called reflection. A straw in a glass of water appears bent because light from the straw refracts as it passes from water into air. The light slows down when entering the denser water and speeds up when leaving, causing the rays to bend. Our brain assumes light travels in straight lines, so the straw appears to be in a different position than it actually is.
Short Answer 3
Model answer: The student should organise the data in a table with columns for material and wave speed, then plot a bar graph to visualise the comparison. They should check for a clear trend: as the density of the material increases, sound speed increases. The evidence-based conclusion should state: "The data shows that sound travels fastest through glass (4 800 m/s), slower through water (1 450 m/s), and slowest through air (330 m/s). This supports the conclusion that wave speed increases as the density of the medium increases." The student should also note any limitations, such as not controlling temperature.