Developing an idea of Laville and Soedel [J. Sound Vib., 60 (1978) 273
1, the noise radiated by the exhaust system of a four cylinder engine
is calculated, analytically and numerically, and compared to experimen
t. The basic idea is as follows: the effect of the exact shape of the
volume velocity signal produced by a cylinder during opening can be co
nsidered as a second order effect on the result. The amplitude of ever
y harmonic of the radiated noise is shown to be proportional to the fi
rst order of certain quantities, the zeroth order being zero. On the o
ne hand, the harmonics H-2, H-4, ... are proportional to the deviation
of the signal during opening from a square signal and to the ratio of
the overlap time of opening of two cylinders to the valve opening dur
ation. On the other hand, the other harmonics are proportional to quan
tities like the ratios of the length difference between two parallel t
ubes of the manifold to the wavelength. The analysis of the amplitude
of the radiated noise exhibits the role of the resonances of the admit
tance of the whole exhaust as viewed from outside when the cylinders a
re closed, and of the resonances of the manifold. Comparison with expe
riment confirms the basic hypothesis and the result of the theory, al
least qualitatively, but losses seem to cancel the manifold resonances
, which are related to the interferences between parallel tubes.