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Basic Sound Calculations

The natural resonant frequency of a material is based on its physical dimensions and the speed of sound in the material (‘c’). The frequency constant (N) is defined as the controlling dimension (t) multiplied by the frequency (Fr):

N = Fr x t

Eqn. 1

The time required to complete a full cycle (i.e. one wavelength) is the period (T), measured in seconds. The relation between frequency and period in a continuous wave is given in Equation (2).

f = 1/T

Eqn. 2

The velocity of ultrasound (c) in a perfectly elastic material at a given temperature and pressure is constant. The relation between c, f, λ and T is given by Equations (3) and (4):

λ = c/f

Eqn. 3

λ = cT

Eqn. 4

The nondestructive ultrasonic testing process is based on the introduction of high frequency sound waves into an object to obtain information. These high frequency sound waves do not alter or damage the object in any way. The “time of flight” (the amount of time required for the sound to travel through the object) and the “amplitude of the received signal” are the two primary measurements critical in ultrasonic testing. Thickness can be determined based on the velocity and the round trip time of flight through the object, as follows:

t = cTf/2

Eqn. 5

Measurements of the relative change in signal amplitude can be used in sizing flaws or measuring the attenuation of a material. The relative change in signal amplitude is commonly measured in decibels. Decibel values are the logarithmic value of the ratio of two signal amplitudes. This can be calculated using the following equation. Some useful relationships are also displayed in the table below:

dB = 20log10(A1/A2)

Eqn. 6

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