Speed of Sound in Solids

The situation with solids is considerably more complicated, with different speeds in different directions, in different kinds of geometries, and differences between transverse and longitudinal waves. Nevertheless, the speed of sound in solids is larger than in liquids and definitely larger than in gases.

Young's Modulus for a representative value for the bulk modulus for steel is 160 $10^9$ N /$m^2$ .

Table 3.3: Solids speed of sound, after Aldred, John, Manual of Sound Recording, London:Fountain Press, 1972

material	reference	Value [m/sec]
Diamond		12000
Pyrex glass		5640
Steel	longitudinal wave	5790
Steel	transverse shear	3100
Steel	longitudinal wave (extensional wave)	5000
Iron		5130
Aluminum		5100
Brass		4700
Copper		3560
Gold		3240
Lucite		2680
Lead		1322
Rubber		1600

Speed of sound in solid of steel, using a general tabulated value for the bulk modulus, gives a sound speed for structural steel of

$$c = \sqrt{ E \over \rho} = \sqrt{160 \times 10^{9} N/m^{2} \over 7860 Kg /m^3} = 4512 m/s$$ (3.38)

Compared to one tabulated value the example values for stainless steel lays between the speed for longitudinal and transverse waves.