Speed_of_sound Sound

u.s. navy f/a-18 approaching speed of sound. white halo formed condensed water droplets thought result drop in air pressure around aircraft (see prandtl-glauert singularity).

the speed of sound depends on medium waves pass through, , fundamental property of material. first significant effort towards measurement of speed of sound made isaac newton. believed speed of sound in particular substance equal square root of pressure acting on divided density:

c
=



p
ρ






{\displaystyle c={\sqrt {p \over \rho }}\,}

this later proven wrong when found incorrectly derive speed. french mathematician laplace corrected formula deducing phenomenon of sound travelling not isothermal, believed newton, adiabatic. added factor equation—gamma—and multiplied





γ





{\displaystyle {\sqrt {\gamma }}\,}








p
ρ






{\displaystyle {\sqrt {p \over \rho }}\,}

, coming equation



c
=


γ
⋅


p
ρ







{\displaystyle c={\sqrt {\gamma \cdot {p \over \rho }}}\,}

. since



k
=
γ
⋅
p



{\displaystyle k=\gamma \cdot p\,}

, final equation came



c
=



k
ρ






{\displaystyle c={\sqrt {\frac {k}{\rho }}}\,}

, known newton-laplace equation. in equation, k = elastic bulk modulus, c = velocity of sound, ,




ρ



{\displaystyle {\rho }}

= density. thus, speed of sound proportional square root of ratio of bulk modulus of medium density.

those physical properties , speed of sound change ambient conditions. example, speed of sound in gases depends on temperature. in 20 °c (68 °f) air @ sea level, speed of sound approximately 343 m/s (1,230 km/h; 767 mph) using formula v = (331 + 0.6 t) m/s . in fresh water, @ 20 °c, speed of sound approximately 1,482 m/s (5,335 km/h; 3,315 mph). in steel, speed of sound 5,960 m/s (21,460 km/h; 13,330 mph). speed of sound sensitive, being subject second-order anharmonic effect, sound amplitude, means there non-linear propagation effects, such production of harmonics , mixed tones not present in original sound (see parametric array).