The principle of superposition for waves states that the resultant displacement at a point is:

A siren emitting at 600 Hz approaches a stationary observer at 30 m/s. If the speed of sound is 330 m/s, the observed frequency is:

An observer moves directly away from a stationary source at speed $v_o$. The apparent frequency is (sound speed $v$, source frequency $f$):

A source approaches a stationary observer. The frequency heard by the observer compared to the source frequency is:

The fundamental frequency of a pipe closed at one end, of length $L$, is:

The fundamental frequency of an open organ pipe of length $L$ (sound speed $v$) is: