In this paper the term hyperbolic horn is used to designate those horns whose area law is given by:S(x) = πR02[coshax+T sinhax]2. WhereS(x) is the cross‐sectional area of the horn at distance (x) from the throat, (a) is the flare constant; (T) is the shape parameter and (R0) is the throat radius.The pressure on the axis due to a circular mouth, unbaffled horn loudspeaker is derived. In this calculation use is made of the recent results of Levine and Schwinger [Phys. Rev.73, 383 (1948)] and some useful additional functions are computed from their data and presented here in graphical form.It is shown how to calculate the frequencies at which peaks occur in hyperbolic horn type loudspeaker frequency response curves.It is shown how to calculate the parameters of hyperbolic and exponential horn type loudspeakers having pre‐determined peaks in their frequency response curves.Some experimental confirmation of the theory is presented.