Passive coupling of the electron cyclotron and synchronous waves in quadrupolar pump fields is examined. It is shown that sinusoidal energy exchange occurs when the quadrupole field is pumped so that the effective or Doppler‐shifted pump frequency as observed by the drifting beam equals the electron cyclotron frequency. One fast and one slow wave are coupled when the pump frequency is greater than either of the beam wave frequencies, while two fast or two slow waves are coupled when the pump frequency is less than at least one of the beam wave frequencies. Experimental results confirming these predictions are presented and possible applications are discussed. In addition, it is shown that active coupling of two synchronous waves occurs when the effective pump frequency is zero.