J.H. Janssen 323 
where now the reference value vy is given by 
Po 
Pwlhw 
Vo = = 13.107" 2 (3) 
if underwater noise reduction is considered (p,c,, is the characteristic imped- 
ance of sea water). It follows that L, =L, for plane traveling waves. This con- 
venient choice of po and vo is applied in this paper. 
The response of mechanical structures to alternating forces can be investi- 
gated either by means of discrete frequency excitation or by means of random 
frequency-mixture excitation (noise). The vast amount of information obtained 
from discrete frequency responses may be reduced in most instances by aver- 
aging over certain adjacent frequency bands. The same "data reduction" is per- 
formed at once if filtered noise bands are used. Bandwidths half an octave wide 
are very convenient: they offer sufficient information in only 16 bands for the 
audio-frequency range. Of course, the time required for an 8-octave-band re- 
sponse measurement is shorter still; too much detail is lost, however. The 
half-octave-band measurement, as reported here, seems to be a good compro- 
mise between discrete frequency (or one-third-octave measurements) and the 
octave-band method. 
Noise may be supposed to consist of many random discrete frequency com- 
ponents. Within a given frequency band, the components of a "noise force" are 
numbered 1,2,3,4,...,n. For a half-octave band the highest frequency f#, is 
equal to or lower than ¥2 times the lowest component frequency f,. The "effective 
value" F.., (time rms) of a noise force is given by 
Fen= (Pi + P34 F3+--) (4) 
where the signa indicates the maximum value (amplitude) of a force component. 
If very many components are present, we may suppose that Eq. (4) can be written 
in the form of an integral 
2 fo 2 
F eg = f F; df (5) 
fa 
where F? is called the spectral density of the force. If a force of this type acts 
upon a mechanical structure, the resulting velocity is of interest. For example, 
the velocity at the excitation point can be found from the usual mechanical input 
impedance defined as the complex ratio of sinusoidal force to velocity, Z = R + jx. 
The expression for the effective value v., of the "noise velocity" reads 
fy - 
ae F 5 df 
eff = 2 2 6 
R?4X (6) 
In this way, a kind of averaged-out impedance—or in general system response— 
may be obtained without going into all details ‘of the discrete frequency analysis. 
A similar result could also be obtained, however, by such an analysis: if the 
system response, e.g., the impedance Z,, were known for very many closely 
spaced frequencies (numbered n), then the ratio of Eq. (6) to Eq. (5) would be 
obtained by averaging all1/|Z,,|’. 
