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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Page discussing the principles of single and double resonance exhaust silencers.

Identifier  ExFiles\Box 104\2\  scan0036
Date  1st July 1932
  
-2-

Again, to deal with low notes (and it will be shown later that some of the exhaust booms are a very low frequency) the single resonator becomes exceedingly large, because the conductivity of the throat has to be high to ensure that too much restriction does not take place. As an example, for a frequency of 80/sec., the single resonating chamber would have to have a capacity of no less than 600 cu.ins. or half the size of the P.II short type silencer to deal with a single boom period.

This is the reason why the single resonator, though its principle was established by Lord Rayleigh, has not been more widely used.

During the last two years, the Americans have developed the double resonance silencer. This is simply two single resonance chambers in series. The effect of putting

INTAKE C₁ N₁ c₂ N₂

two such chambers in series is to produce two response frequencies, one below the frequency of the large chamber and one above the frequency of the small chamber i.e. two small chambers can damp as low a note as one very large one. At the same time the range over which the silencer is effective is greatly increased, though the peak damping is not so pronounced. This is illustrated in Sheet 1. The character of the response and its amplitude is not truly shown in the curve as it is modified by the damping introduced; the frequencies of maximum response, however, can be calculated from the equation. Sheet 2, shows the method of finding the sizes of chambers and their conductivities to deal with two boom periods, one at 54 and the other at 140/sec.

Practice differs somewhat widely from theory and we find the quickest and simplest result is obtained on an exhaust silencer by having a number of chambers connected by
  
  


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