PX154 - G4 - three dimensional solids - bulk waves

in solids, we need to consider both compressional (longitudinal) waves, and shear (transverse) waves
now, we use the bulk modulus: $- V \frac{\partial p}{\partial V}$ , where $V = v o l u m e$ , $p = p r e s s u r e$ [YF fig 11.17]
we can consider two wave speed:
- compressive waves (often called "p waves"):
$v_{p} = \sqrt{\frac{B + \frac{4 G}{3}}{ρ}}$
- shear waves (often called "s-waves"):
$v_{s} = \sqrt{\frac{G}{ρ}}$ - do not travel through liquids
eg: for earth, $B = 105 G P a$ , $B = 5 G P a$ ("typical")
$v_{p} = 7.7 \times 10^{4} m^{- 1}$
$v_{s} = 4.3 \times 10^{3} m s^{- 1}$
determined earth's internal structure by studying waves
also, ultrasound