Let a particle of charge e and rest mass m, initially at rest in the laboratory, scatter a photon of initial frequency v_i. this is called compton scattering. suppose the scattered photon comes off at an angle theta from the incident direction. use conservation of four-momentum to deduce that the photon's final frequency v_f is given by 1/v_f = 1/v_i + h (1-cos theta/m)

The speed of sound is through a solid is calculated using

where Y is the young Modulus and d is the density.

And no, the other answer is wrong. Density is only part of the reason why sound is faster through steel than wood, but the reason why sound through steel is faster is because steel has a higher young modulus (Y) value than wood.

Lead has a higher density than steel but is slower for sound to go through because lead has a lower Y value.