The physics
Two notes close in pitch sound like one tone. Its loudness swells and fades again and again. Each swell is one beat.
fb = |f₁ − f₂|
Wax makes a fork heavier, so it rings lower. Filing a fork makes it ring higher. Watch the beats after the change. They show which side of the other fork it sat on.
A moving source or a moving listener changes the pitch you hear. This is the Doppler effect. Two notes that start equal can then beat.
f′ = f (v + vo)/(v − vs)
An echo from a moving wall shifts twice. The wall hears a shifted note, then sends it back as a moving source.
fecho = f (v + u)/(v − u)