Amplitude, Wavelength and Frequency
In 1973, physicist Jearl Walker showed that a 440 Hz violin A-string drops to 220 Hz if you double its vibrating length — exactly one octave lower.
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Q1 · What happens to the pitch of a guitar string when you make it shorter or tighter?
Q2 · If you double the frequency of a wave but keep the speed the same, what do you think happens to the wavelength?
● Know
- Amplitude is the maximum displacement from the rest position.
- Wavelength is the distance between two consecutive corresponding points on a wave.
- Frequency is the number of waves passing a point per second, measured in hertz (Hz).
● Understand
- Amplitude relates to wave energy, wavelength relates to wave spacing, and frequency relates to how often waves occur.
● Can do
- Measure and calculate amplitude, wavelength, and frequency from wave diagrams.
Hold a tuning fork against a bench top and tap it: the fork vibrates exactly 440 times every second if it is tuned to concert A, and that rapid back-and-forth motion is what you hear as a steady pitch. The number of complete cycles passing a fixed point each second is called frequency, measured in hertz (Hz). Frequency is what your brain interprets as pitch for sound and colour for light.
When a violinist shortens a string by pressing it against the fingerboard, the vibrating portion becomes shorter. A shorter string vibrates faster, which means higher frequency and higher pitch. This is why the same string produces a higher note when shortened. The relationship between length and frequency is inverse: half the length approximately doubles the frequency.
For light, frequency determines colour. Red light has the lowest visible frequency, around 400 trillion Hz. Violet light has the highest visible frequency, around 750 trillion Hz. Beyond violet lies ultraviolet; below red lies infrared. Both are invisible but are still electromagnetic waves.
A standard Australian electrical mains supply oscillates at 50 Hz. A typical mosquito buzzes at around 600 Hz, and a dog whistle produces sound near 25,000 Hz. The frequency difference is enormous: the dog whistle vibrates 500 times faster than mains electricity.
Australian wildlife acoustics: Researchers at the University of Queensland study the low-frequency infrasound calls of cassowaries, which fall below 20 Hz. These calls travel long distances through rainforest. Understanding frequency helps biologists track populations and design conservation strategies.
Higher frequency means louder sound. Frequency and amplitude are independent. Frequency determines pitch; amplitude determines loudness. A high-frequency sound can be quiet, and a low-frequency sound can be loud. Confusing pitch and volume is one of the most persistent errors in wave physics.
Rank these wave sources from lowest to highest frequency.
- Infrasound elephant call
- Human voice speaking
- Dog whistle
- Visible green light
- Medical X-ray
Wavelength, symbolised by lambda (λ), is the distance between two identical points on adjacent cycles. You can measure it from crest to crest, trough to trough, or any corresponding point. Wavelength is measured in metres, though for light it is often measured in nanometres.
Wavelength and frequency are intimately related through wave speed. For any given medium, wave speed is roughly constant. This means if frequency increases, wavelength must decrease to compensate. A high-pitched sound has a short wavelength; a low-pitched sound has a long wavelength.
This inverse relationship explains why bass speakers are large (they need to move lots of air for long wavelengths) while tweeters are small (they produce short wavelengths). It also explains why AM radio waves (low frequency, long wavelength) diffract around hills while FM waves (high frequency, short wavelength) need line-of-sight.
In air, sound travels at about 340 m/s. A note with frequency 170 Hz has wavelength λ = 340/170 = 2 metres. A note with frequency 340 Hz has wavelength 1 metre. If you double the frequency, you halve the wavelength. This is why bass notes seem to wrap around corners, while high notes are more directional.
ARIA radio broadcasting: Australian AM radio stations broadcast around 1000 kHz, giving wavelengths of about 300 metres. FM stations broadcast near 100 MHz, with wavelengths around 3 metres. AM signals travel further at night; FM provides higher-fidelity local coverage. Engineers choose frequencies based on wavelength behaviour.
Wavelength and frequency are unrelated. In a given medium, speed is fixed by the medium properties. Changing frequency always changes wavelength, and vice versa. The relationship v = fλ is a mathematical law, not a rough guideline.
Amplitude measures how far a wave swings from its rest position. In a transverse wave, it is the height from the middle line to a crest. In a longitudinal wave, it corresponds to the maximum pressure difference. Amplitude is directly related to the energy carried by a wave.
A wave with twice the amplitude carries four times the energy. This is why a small increase in amplitude produces a large increase in loudness or brightness. It is also why loud sounds can damage hearing: the high amplitude transfers enough energy to physically damage delicate structures in the inner ear.
Amplitude is independent of frequency and wavelength. You can have a loud low note, a quiet high note, a bright red light or a dim blue light. Amplitude tells you about energy; frequency tells you about type or pitch.
When you turn up the volume on your headphones, you increase the amplitude of the sound waves reaching your ears. The frequency stays exactly the same, but each compression pushes harder and each rarefaction pulls harder. Your eardrum moves further in response, and your brain interprets this as louder sound.
Australian workplace safety: Safe Work Australia sets noise exposure limits based on sound amplitude, measured in decibels. Workers must wear hearing protection when sound levels exceed 85 dB. The regulations exist because high-amplitude sound waves transfer enough energy to cause permanent hearing loss.
If I make a sound louder, the pitch goes up too. Many people unconsciously link loudness and pitch. But they are controlled by different properties. A bass guitar can be painfully loud without ever becoming high-pitched. A flute can be whisper-quiet while still playing a high note.
is the from the rest position. It determines the of a sound and the of a light.
The three wave properties are linked by v = fλ. This equation is universal: it applies to sound, light, water waves and every periodic wave. If you know any two quantities, you can calculate the third.
Wave speed is determined primarily by the medium, not by the source. Sound travels at about 340 m/s in air, regardless of whisper or shout. In water, sound travels about four times faster. Light travels at 3 × 10⁸ m/s in a vacuum, slowing slightly in transparent materials.
Because speed is fixed by the medium, changing the frequency in a given medium always changes wavelength in the opposite direction. A high-frequency sound in air has a short wavelength; a low-frequency sound has a long wavelength. The product fλ stays constant.
A radio station broadcasts at 100 MHz. Radio waves travel at 3 × 10⁸ m/s. The wavelength is λ = v/f = 3 × 10⁸ / 1 × 10⁸ = 3 metres. This is why FM radio antennas are often about 3 metres long: they are designed to resonate with the wavelength.
Australian mobile networks: Telstra, Optus and Vodafone operate at various frequencies including 700 MHz, 1800 MHz and 2600 MHz. Lower frequencies have longer wavelengths and travel further, ideal for rural coverage. Higher frequencies carry more data, better for cities. The v = fλ relationship shapes Australia telecommunications infrastructure.
Higher frequency waves always travel faster. In a given medium, all waves of the same type travel at the same speed. A high-pitched sound does not reach you before a low-pitched sound from the same source. They arrive together because v is fixed by the air.
Complete this wave speed calculation.
Using v = f × λ, the wave speed is v = × = m/s.
By now you have met the four essential descriptors of any wave: frequency, wavelength, amplitude and speed. Each describes a different aspect, and together they give a complete picture. A scientist analysing an unknown wave will measure these four quantities first.
Frequency and wavelength are linked through speed. Amplitude stands alone, telling you about energy. Speed is determined by the medium. When you change one property, you must consider consequences. Shortening a violin string increases frequency and decreases wavelength, but does not change amplitude or speed.
These terms are tools for prediction. If you know a sound wave has frequency 1000 Hz and speed 340 m/s, you know its wavelength is 0.34 m. If you know a light wave has wavelength 500 nm and speed 3 × 10⁸ m/s, you know its frequency is 6 × 10¹⁴ Hz.
A dolphin produces clicks at 150 kHz for echolocation. In seawater, sound travels at about 1500 m/s. The wavelength is λ = 1500/150,000 = 0.01 m = 1 cm. This short wavelength allows dolphins to detect small objects. If the wavelength were much longer, the sound would diffract around small objects instead of reflecting back.
Australian Institute of Marine Science: Researchers studying the Great Barrier Reef use sonar with carefully chosen frequencies and wavelengths. Low-frequency sonar penetrates deep into sediment. High-frequency sonar resolves fine coral details. Selecting the right wavelength is essential for mapping reef health.
Amplitude affects wavelength. Amplitude, frequency and wavelength are independent in the sense that changing amplitude does not change frequency or wavelength. However, frequency and wavelength are linked through the medium wave speed. Making a wave bigger does not make it longer or faster.
- Frequency
- Wavelength
- Amplitude
- Speed
- Cycles per second (Hz)
- How fast the wave travels (m/s)
- Distance per cycle (m)
- Maximum displacement from rest
Measuring wave speed connects the abstract equation v = fλ to concrete measurement. The simplest method is distance and time: if sound travels 100 metres in 0.29 seconds, its speed is about 340 m/s. You can also measure frequency and wavelength separately, then multiply them.
For sound, a good classroom method uses two people and a long corridor or oval. One person makes a sharp sound and a visible signal simultaneously. The second person starts a timer on seeing the signal and stops on hearing the sound. The time difference is effectively the sound travel time.
For waves on a string, measure wavelength with a ruler and frequency with a timer. Multiplying gives wave speed. Changing the tension changes the speed, which is why guitarists tighten strings to tune them.
A student measures two consecutive compressions on a slinky 15 cm apart. They time 10 compressions passing in 2.5 seconds, giving frequency 4 Hz. Wave speed v = 4 × 0.15 = 0.6 m/s. Stretching the slinky tighter increases the speed because the medium tension has changed.
Australian sports timing: At athletics meets, officials use electronic timing detecting sound and light from the starting gun. Because light travels almost a million times faster than sound, electronic systems use the light signal to avoid the speed-of-sound delay affecting manual timing.
I can measure wave speed by timing how long one crest takes to travel. This works in principle, but crests are hard to track. It is much easier to measure wavelength and count crests per second, then multiply. Choose the method giving the most accurate result with available equipment.
You learned that amplitude measures wave energy, wavelength measures wave spacing, and frequency measures how many waves pass per second.
A wave has an amplitude of 3 cm and a frequency of 2 Hz. If the amplitude is doubled but frequency stays the same, what happens to the energy of the wave?
At the start of the lesson, you heard about the Sydney Opera House Concert Hall — how engineers tuned amplitude and frequency so musicians could hear every note clearly.
Now that you can define amplitude, wavelength and frequency precisely, how would you explain what those engineers actually adjusted? Did anything about those three measurements surprise you?
1. What is the unit of frequency?
2. Which wave property is related to the energy carried by the wave?
3. If 8 waves pass a point in 4 seconds, what is the frequency?
4. What does the Greek letter λ (lambda) represent?
5. A wave with a higher frequency will have:
Define amplitude, wavelength, and frequency, and state the unit for each. (3 marks)
Hint: Make sure to include the symbols λ and Hz.
A wave has a period of 0.25 seconds. Calculate its frequency. Show your working. (3 marks)
Hint: Use the formula f = 1 / T.
Explain why a loud sound has a larger amplitude than a quiet sound, using the terms energy and displacement. (3 marks)
Hint: Link amplitude to the maximum displacement of air particles.