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Sound Waves
Waves & Optics
Sound is a longitudinal wave of compressions and rarefactions travelling through a material. Its frequency sets its pitch, its amplitude sets its loudness, and its speed depends on the medium.
How sound travels
Sound is produced when an object vibrates, pushing nearby air particles back and forth. The vibrations create regions of high pressure, called compressions, and regions of low pressure, called rarefactions, which travel outward as a longitudinal wave. The particles themselves only oscillate about their rest positions; it is the pattern of pressure that moves. Sound needs a medium: it travels through air, water and solids, but not through a vacuum. The speed depends on the medium and its temperature, because stiffer and denser materials transmit vibrations differently. In air at 20 degrees C it is about 343 m/s, far slower than light.
Pitch, loudness and quality
Frequency determines pitch: a higher frequency sounds higher, and the human ear can hear roughly 20 Hz to 20,000 Hz. Amplitude determines loudness: a larger vibration carries more energy and sounds louder, measured in decibels. The quality or timbre of a sound depends on its waveform, which is why a violin and a flute playing the same note sound different: each produces the same fundamental frequency plus a different mixture of overtones. Ultrasound is sound above 20,000 Hz, too high for humans to hear, while infrasound is below 20 Hz. Bats and dolphins use ultrasound for echolocation.
Where you see it
Echoes are sound waves reflected from a surface, and bats, ships and medical scanners all use them to judge distance: the longer the delay, the farther the reflecting object. Ultrasound scans build images of a baby in the womb or of organs inside the body without harmful radiation. Sonar maps the seabed and finds shoals of fish. Noise-cancelling headphones use destructive interference to cancel unwanted sound. Concert halls are designed so that reflections reinforce the music rather than blurring it, and an empty room echoes because hard walls reflect sound strongly.
📝 Worked example: wavelength of a musical note
A musical note has frequency f = 440 Hz, the note A above middle C. Speed of sound in air v = 343 m/s. Use wavelength lambda = v / f. Substitute: lambda = 343 / 440 = 0.78 m. So the wavelength of the note is about 0.78 m. A lower note of 220 Hz would have twice the wavelength, about 1.56 m, at the same speed.
Common mistakes
- Thinking sound is transverse: sound in air is longitudinal; the air vibrates back and forth along the direction the sound travels.
- Confusing loudness with pitch: loudness depends on amplitude, pitch depends on frequency.
- Assuming sound travels at the same speed everywhere: it is about 343 m/s in air, about 1500 m/s in water, and faster still in steel.
Practice questions
- What is the wavelength of a 256 Hz note in air, where sound travels at 343 m/s?
Show answer
lambda = 343/256 = 1.34 m.
- Estimate the speed of sound in air at 20 degrees C.
Show answer
v = 331 + 0.6 x 20 = 331 + 12 = 343 m/s.
- Lightning is seen 1000 m away. Roughly how long before the thunder is heard?
Show answer
About 2.9 s, because sound takes about 1 s to travel 343 m, so 1000/343 is about 2.9 s.
Frequently asked questions
Can sound travel through space?
No. Sound needs a medium of particles to vibrate; in the vacuum of space there is nothing to carry it, so space is silent.
Why can you sometimes hear distant sounds better at night?
Because sound travels faster in warm air, the top of a wavefront can outrun the bottom, bending the sound back down toward the ground.