AbstractWe discuss the asymptotic behaviour of acoustic and electromagnetic waves, generated by given time‐harmonic exterior forces with frequency ω, in the unbounded region between the parallel planesX3= 0 andX3= 1, and show that the principle of limiting amplitude is violated if ω = πn(n= 1, 2,…). For these values of the frequency, forces with compact support can be chosen such that the amplitudes of the waves increase with a logarithmic rate