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Waves and Sound: Frequency, Wavelength, and Speed

Waves are disturbances that transfer energy from one place to another without permanently displacing the medium. Understanding waves is essential for explaining sound, light, earthquakes, and the behaviour of electrons in atoms.

What Is a Wave?

When you drop a stone into a still pond, ripples spread outward. The water itself does not travel to the shore — individual water molecules move up and down (or in circular paths) while the pattern of disturbance travels outward. This is the defining feature of a wave: it carries energy, not matter.

Every wave has five key properties:

• Amplitude (A): the maximum displacement of the medium from its rest position. For a water wave, it is the height from calm surface to crest. Greater amplitude means more energy.
• Wavelength (λ): the distance between two consecutive identical points on a wave — crest to crest, or trough to trough. Measured in metres.
• Frequency (f): the number of complete wave cycles passing a fixed point per second. Measured in hertz (Hz), where 1 Hz = 1 cycle per second.
• Period (T): the time taken for one complete wave cycle. T = 1/f.
• Wave speed (v): how fast the wave pattern moves through the medium.

The Wave Equation

The three properties — speed, frequency, and wavelength — are linked by the wave equation:

v = f λ

In words: wave speed equals frequency times wavelength. If a sound wave has a frequency of 440 Hz and a wavelength of 0.773 m, its speed is 440 × 0.773 ≈ 340 m/s — the approximate speed of sound in air at room temperature.

Rearranging the equation is often necessary in problems: λ = v/f (to find wavelength) and f = v/λ (to find frequency). The wave speed for a given type of wave in a given medium is fixed — changing frequency changes wavelength inversely, but not speed.

Transverse and Longitudinal Waves

Waves are classified by the direction of their oscillation relative to the direction of travel.

In a transverse wave, the particles of the medium oscillate perpendicular to the direction the wave travels. Light waves and electromagnetic waves in general are transverse. The S-waves (secondary waves) generated by earthquakes are transverse mechanical waves that travel through rock. Waves on a guitar string are transverse.

In a longitudinal wave (also called a compression wave), the particles oscillate parallel to the direction of travel, creating alternating regions of compression (particles pushed together) and rarefaction (particles pulled apart). Sound is a longitudinal wave. Earthquake P-waves are also longitudinal.

Sound Waves in Detail

Sound is produced when a vibrating object (a speaker cone, a vocal cord, a struck bell) pushes and pulls the surrounding air molecules. The compression and rarefaction regions spread outward as a longitudinal pressure wave. When this wave reaches the eardrum, it causes the eardrum to vibrate at the same frequency, which the brain interprets as sound.

Pitch corresponds to frequency: a higher frequency produces a higher-pitched sound. The human ear can typically detect frequencies from about 20 Hz to 20,000 Hz (20 kHz). Sound below 20 Hz is infrasound (felt rather than heard; produced by large events like earthquakes and thunder). Sound above 20 kHz is ultrasound (used in medical imaging and by bats for echolocation).

Loudness corresponds to amplitude: greater air pressure variation produces louder sound. Loudness is measured in decibels (dB) on a logarithmic scale. A normal conversation is about 60 dB; a jet engine at 30 metres is about 140 dB, which can cause immediate hearing damage.

Speed of Sound in Different Media

The speed of sound depends on the elasticity and density of the medium. Tightly packed particles transmit pressure disturbances more efficiently, so sound generally travels faster in denser, more elastic materials:

• Air at 20°C: approximately 343 m/s
• Water at 20°C: approximately 1,480 m/s
• Steel: approximately 5,100 m/s
• Glass: approximately 5,300 m/s

This is why pressing your ear against a metal rail lets you hear a distant train long before you hear it through the air. Temperature also affects sound speed in gases: in air, speed increases by about 0.6 m/s for every 1°C rise in temperature.

Reflection, Refraction, and Diffraction

Reflection occurs when a wave bounces off a boundary. Echoes are reflected sound waves; mirrors reflect light waves. The law of reflection states that the angle of incidence equals the angle of reflection.

Refraction is the bending of a wave as it passes from one medium into another where it travels at a different speed. Light bends when it enters glass from air; this is why a straw appears bent in a glass of water.

Diffraction is the spreading of a wave as it passes through a gap or around an obstacle. Sound diffracts easily around corners (you can hear someone in the next room even without line of sight) because sound wavelengths — centimetres to metres — are comparable to everyday object sizes. Light diffracts far less noticeably in everyday life because its wavelengths (400–700 nanometres) are tiny.

The Doppler Effect

When a wave source is moving relative to an observer, the observed frequency differs from the emitted frequency. As a sound source approaches, the sound waves in front of it are compressed together — an observer in front hears a higher pitch. As the source passes and moves away, the waves are stretched — the observer hears a lower pitch. This is the Doppler effect, experienced every time an ambulance drives past. Police radar guns and weather Doppler radar use this principle to measure speed.

Summary

Waves transfer energy without permanently moving matter. The wave equation v = fλ links wave speed, frequency, and wavelength. Transverse waves oscillate perpendicular to their direction of travel; longitudinal waves (including sound) oscillate parallel to it. Sound speed varies with medium density and elasticity. Reflection, refraction, and diffraction describe wave behaviour at boundaries and obstacles. The Doppler effect shifts the observed frequency of a wave when the source moves relative to the observer.