J, H. Janssen 327 
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Fig, 17.5. For “normal” excitation, two isolation curves were determined: (A) exciter position in the 
middle of a steel bar resting on two rubber blocks on a 4-m I-NP-16-beam, and (B) exciter position 
above one of the rubber blocks. From the stiffness of the blocks (~2.5° 10* N/m per block) and the 
impedance level of the beam (L,,, shown in figure), an approximate isolation curve may be computed 
which agrees fairly well with curve A. The exciter position clearly influences the experimental result; 
additional rotation of a spring contact plane presumably increases the velocity level L,, of the beam. 
Sinusoidal plane waves may exist in the plate or beam. For the bending wave 
velocity cg one finds that 
cp =V27 fc, ty (13) 
where c, =\VE/p, the longitudinal plane wave velocity in the material; and 1, is 
the so-called radius of gyration, equal to \I/A. For plates, this radius of gyra- 
tion is given by 
i, -—4 (14) 
where h is the plate thickness; for beams, i, may be found in tables or hand- 
books. 
In Fig. 17.6 the bending wavelength \g=c,/f is shown as a function of the 
frequency f and the plate thickness A for three common building materials, The 
longitudinal wavelength for sinusoidal plane waves in air and in sea water is 
also shown. For the greater part of the audio-frequency range, A, is smaller 
than A in sea water. This fact has an important bearing on the sound radiation 
by shell plates into water, and itcanbe understood in a qualitative way as follows. 
Suppose two loudspeakers are mounted close together inone baffle. They vibrate 
in opposite phase. If the distance between the speakers is less than the wave- 
length in the surrounding air, the sound radiation is very inefficient because of 
