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Wave speed in a medium
Intermediate
Depends on elasticity and density.
v = √(B/ρ)Generally v = √(elastic modulus / density): for sound in a fluid v = √(B/ρ), in a solid rod √(Y/ρ). Stiffer, lighter materials are faster.
Sound in steel 5000 m/s, in water 1480 m/s, in air 343.
More elastic gives higher speed.
In more detail
The speed of a wave depends on the stiffness and inertia of the medium. For a longitudinal wave in a fluid, v = sqrt(B/ρ), where B is the bulk modulus and ρ is the density.
Real-world uses
- Sound travels faster in water than in air because water is much stiffer.
- Seismologists estimate rock properties from wave speeds.
- Seismologists use the speed of sound in rock to estimate the depth of an earthquake's source.
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Frequently asked questions
Why is sound faster in water?
Water is much less compressible, which gives a larger bulk modulus relative to density.
Does frequency change the speed?
In most media, no. Only in dispersive media does speed depend on frequency.
Why do sound waves move faster in solids?
Solids are stiffer, so the elastic restoring force is larger, and the wave travels faster even though solids are denser.
Related topics in Waves & Sound
Wave equation (travelling) · Wave number · Wave speed on a string · Speed of sound · Speed of sound in gases · Reflection of waves