A liquid heating apparatus of the type which includes a liquid vessel assembled within a support frame, a pulse combustion burner mounted to the vessel and having a combustion chamber secured at its inlet end to a side wall of the vessel and immersed in liquid in the vessel, a tailpipe connected at its one end to an exhaust port of the combustion chamber and being extended outwardly through the vessel, and an exhaust muffler assembly connected to an exhaust end of the tailpipe. The exhaust muffler assembly includes a plurality of mufflers connected in series to the exhaust end of the tailpipe, a final one of the mufflers being in the form of a resonance type muffler for reducing low frequency noises caused by pulse combustion in the combustion chamber. The final one of the mufflers is detachably mounted in place at the outside of the support frame for easy replacement with another resonance type muffler and connected to the preceding muffler in a disengageable manner.