Why is a tuning fork made of steel and sonometer of wood?

Answer 1

If the Fork was made of Wood you wouldn't get a sound.

If the Sonometer was made of Steel,.. you wouldn't want to haul it around.

(SOME)Steel doesn't rust. [Different Metals can also make different sounds]

Wood is just convient.

Answer 2

A tuning fork is the exciter or the instigator.

A sonometer is the resonator or receiver.

Also - sonometers are old enough that it was by far cheaper to work in wood to accomplish this than metal.

A metal sonometer would give performance similar to the difference between a dobro and an acoustic guitar.