© Schlengermann page 1 of 2

Factors related to beam width of ultrasonic piston oscillators (circular and rectangular)

dB-drop

free-field

dB-drop

echo mode

amplitude ratio

p/p0

factor

kdisk

factor

krectangle

valid for distances

> x D2/4λ

resp. > x A2/4λ

resp. > x B2/4λ

0 0 1.00000 0 0 0.8

0.5 1.0 0.94406 0,21497 0.18599 0.8

1.0 2.0 0.89125 0.30254 0.26150 0.9

1.5 3.0 0.84140 0.36872 0.31839 0.9

2.0 4.0 0.79433 0.42365 0.36547 1.0

2.5 5.0 0.74989 0.47129 0.40616 1.1

3.0 6.0 0.70795 0.51367 0.44224 1.2

3.5 7.0 0.66834 0.55200 0.47477 1.3

4.0 8.0 0.63096 0.58708 0.50444 1.4

4.5 9.0 0.59566 0.61947 0.53173 1.5

5.0 10.0 0.56234 0.64956 0.55699 1.6

6.0 12.0 0.50119 0.70403 0.60248 1.8

7.0 14.0 0.44668 0.75226 0.64244 2.0

8.0 16.0 0.39811 0.79539 0.67790 2.2

9.0 18.0 0.35481 0.83425 0.70958 2.4

10.0 20.0 0.31623 0.86943 0.73803 2.6

12.0 24.0 0.25119 0.93050 0.78678 3.0

20.0 40.0 0.10000 1.09000 0.91000 4.4

∞ ∞ 0 1.21967 1.00000 ∞

© Schlengermann page 2 of 2

Disk oscillator: (p/p0) = 2J1[(π/λ)Dsinγ]/ [(π/λ)Dsinγ] D transducer diameter

sinγ = kdB (λ/D) J1 Bessel’s function

Rectangular oscillator: (p/p0) = sin[(π/λ)Asinγ]/ [(π/λ)Asinγ] (parallel to large side A of transducer)

(p/p0) = sin[(π/λ)Bsinγ]/ [(π/λ)Bsinγ] (parallel to small side B of transducer)

sinγA = kdB (λ/A)

sinγB = kdB (λ/B)

λ wavelength

γ angle of divergence, related to a defined amplitude drop,

measured against beam axis

references

• Krautkrämer, Josef and Herbert:

Ultrasonic testing of materials,

Springer, Berlin (1990) 4th

edition, chapters 4.4, 4.5.

• Schlengermann, Udo:

The Krautkramer Blue Booklet.