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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).
Theory of resonance exhaust silencers, including formulas and experimental results.

Identifier  ExFiles\Box 104\2\  scan0035
Date  1st July 1932
  
To R.{Sir Henry Royce} from Hs{Lord Ernest Hives - Chair}/Hm.{Capt. W. Hallam - Head Repairs}
c. SG.{Arthur F. Sidgreaves - MD} wor.{Arthur Wormald - General Works Manager}
c. RG.{Mr Rowledge} R.{Sir Henry Royce}
c. HY.{Tom Haldenby - Plant Engineer} Ds. Hdy.{William Hardy}

X5230.

Hs{Lord Ernest Hives - Chair}/Hm.{Capt. W. Hallam - Head Repairs}11/ADS.7.32.

RESONANCE EXHAUST SILENCERS.

We have now done sufficient work on these to say something about them. The theory of a resonance silencer is briefly as follows.

The dimensions of a single resonator, closed at its outer end, that will respond to a given tone can be obtained from the formula

N = (A/2π) * √(C/Q)

where N = frequency of the resonator
A = velocity of sound
C = conductivity of the passage connecting the capacity with the source of sound.
Q = volume of the capacity

C = πr² / (L + (π/2)R)

where R is the rad and L is the length of the passage.

We have proved by experiment on the road, that it is possible to tune out a carburetter roar at one particular road speed by having a container attached to the air intake and varying the capacity of the container by means of a moveable plunger.

[Blueprint image of a resonator device]

The difficulty about this is that on a carburetter there is often a wide range of roar and frequently two or more noisy frequencies separated by a considerable range. To silence such an intake by means of single resonators would be rather a formidable proposition. This is even more so on an exhaust silencer, where the exciting impulses are so much greater and boom periods occur at numerous speeds.
  
  


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