Types of Mechanical Waves

The defining question for any mechanical wave is: which direction do the medium's particles move compared with the wave's direction of travel? If the particle motion is at 90° (perpendicular) to the wave's propagation direction, the wave is transverse. If the particle motion is along the same line as propagation — either towards or away from neighbouring particles — the wave is longitudinal.

In a transverse wave you can identify clear crests (highest displacement) and troughs (lowest displacement). The wavelength λ is the distance from one crest to the next. Amplitude A is the maximum displacement from the equilibrium position. Because the oscillations are perpendicular to propagation, transverse waves can exhibit polarisation — the plane of vibration can be restricted to one direction. This is impossible in longitudinal waves. Examples: waves on strings, water surface waves (approximately), seismic S-waves.

In a longitudinal wave, regions of high pressure (compressions) alternate with regions of low pressure (rarefactions). One full wavelength λ equals the distance from one compression to the next — or equivalently, one rarefaction to the next. The amplitude is now the maximum displacement of a particle along the direction of travel, not perpendicular to it. Sound in air, ultrasound in tissue, and seismic P-waves are all longitudinal. Longitudinal waves can travel through solids, liquids, and gases because all three resist being compressed.

Regardless of whether a wave is transverse or longitudinal, all mechanical waves obey the same fundamental relationship: wave speed equals frequency multiplied by wavelength (v = fλ). The speed of the wave depends on the properties of the medium — for example, the tension and linear density of a string for transverse waves, or the bulk modulus and density of air for sound. Changing the medium changes v, which in turn changes λ while f remains fixed (frequency is set by the source, not the medium).

For transverse waves on a string, the wave speed is v = √(T/μ), where T is the tension in the string (in newtons) and μ is the linear mass density (kg per metre). A tighter string or a lighter string transmits waves faster. This is why guitar strings of different thicknesses produce different pitches even when plucked with the same force — the wave speed changes, altering which standing-wave frequencies (harmonics) fit along the string.

Sound speed in an ideal gas is v = √(γP/ρ), where γ is the adiabatic index (≈1.4 for air), P is the ambient pressure, and ρ is the air density. At 20 °C this gives approximately 343 m s⁻¹. Crucially, sound speed increases with temperature because warmer air has greater molecular speed, transmitting compressions more rapidly. This is why thunder from a distant storm arrives seconds after lightning — sound is far slower than light, not because it is longitudinal, but because air is a low-density, compressible medium.

• v — Wave speed (m s⁻¹): The speed at which the wave pattern (crest, trough, compression, or rarefaction) moves through the medium. Determined by the medium's properties, not the source.
• f — Frequency (Hz (s⁻¹)): The number of complete oscillations (cycles) passing a fixed point per second. Set by the source of the wave and unchanged when the wave moves from one medium to another.
• \lambda — Wavelength (m): The distance between two successive identical points on the wave — crest to crest, or compression to compression. Changes when the wave enters a new medium because v changes while f stays constant.

Problem. A student strikes a tuning fork that vibrates at 440 Hz and holds it near one end of a 1.20 m air column. The speed of sound in air is 340 m s⁻¹. (a) Calculate the wavelength of the sound wave produced. (b) State whether this is a transverse or longitudinal wave and justify your answer.

Answer. Wavelength λ = 0.773 m; the wave is longitudinal because particle oscillations are parallel to the direction of propagation.

• Mechanical Waves — Introduction — Establishes what a mechanical wave is and what all waves have in common before distinguishing transverse from longitudinal types.
• Wave Speed, Frequency and Wavelength — The equation v = fλ applies to both transverse and longitudinal waves; this topic explores how each quantity changes in different media.
• Sound Waves — Sound is the primary real-world example of a longitudinal mechanical wave, making it a direct application of the concepts covered here.
• Wave Reflection and Refraction — Both transverse and longitudinal waves reflect and refract at boundaries; understanding wave type is essential before studying these behaviours.
• Standing Waves — Standing waves form in strings (transverse) and air columns (longitudinal); distinguishing wave types explains why the boundary conditions differ.