Longitudinal Wave
Compressions / rarefactions along propagation.
Key Notes
Longitudinal wave: medium particles oscillate PARALLEL to direction of wave propagation.
Examples: sound in air/water, P-waves (compression seismic waves), waves along a Slinky.
Compressions and rarefactions alternate along the wave direction.
Speed in a fluid: v = √(B/ρ), where B = bulk modulus, ρ = density.
Sound in air at 20°C: v ≈ 343 m/s. In water: v ≈ 1500 m/s. In steel: v ≈ 5000 m/s.
CANNOT be polarised — oscillation direction is set by propagation.
Can propagate in solids, liquids, gases — wherever pressure can transmit force.
Same wave equation y(x,t) = A·sin(kx − ωt) but y is now particle displacement along x.
Formulas
Wave-speed in fluid
B = bulk modulus; ρ = density.
Sound in gas (adiabatic)
Air at 0°C: v ≈ 331 m/s. T-dependence: v ∝ √T.
Speed in solid (1D)
Y = Young's modulus for a thin rod.
Pressure wave amplitude
Pressure variation related to particle-displacement gradient.
Important Points
Longitudinal: particle motion PARALLEL to wave. Sound is the canonical example.
Cannot be polarised — direction of oscillation is fixed by propagation.
Sound moves faster in solids than fluids because solids are STIFFER (higher B, Y).
Sound speed in gas grows as √T — twice as fast at very high temperature.
Sound in water ~4.4× faster than in air despite higher density — because B is much larger.
Earth's interior probed by P-waves (longitudinal); they travel through liquid outer core unlike S-waves.
Longitudinal Wave notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.