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Ultrasonic Formula - Signal Amplitude Gain/Loss
Expressed in dB

The dB is a logarithmic unit that describes a ratio of two measurements. The equation used to describe the difference in intensity between two ultrasonic or other sound measurements is:

where: DI is the difference in sound intensity expressed in decibels (dB), P1 and P2 are two different sound pressure amplitude measurements, and the log is to base 10.

For more information on the decibel and its use, take this link.

Exmple Calculation 1
Two sound pressure measurements are made using an ultrasonic transducer. The output voltage from the transducer is 600 mv for the first measurement and 100 mv for the second measurement. Calculate the difference in the sound intensity, in dB, between the two measurements?

Substitute in the voltage values:

Divide to get a decimal value for the ratio:

Take the log of 0.1667:

Multiply:

The sound intensity changed by -15.56dB. In other words, the sound intensity decreased by 15.56 dB

 

Example Calculation 2

If the intensity between two ultrasonic measurements increases by 6 dB, and the first measurement produces a transducer output voltage of 30 mv, what was the transducer output voltage for the second measurement?

Substitute the know information in to the equation:

Divide both sides of the equation by 20

Simplify:

Clear the log:

Simplify:

Solve for P2:

The voltage output for P2 is 60mv.  Notice that a 6dB increase in sound intensity doubled the voltage output.

 

Example Calculation 3

Consider the sound pressure difference between the threshold of human hearing, 0 dB, and the level of sound often produce at a rock concert, 120 dB. (Note: prolonged sound levels above 85 dB are considered harmful, while levels above 120 dB are unsafe.)

where: P1is the sound pressure of the reference level, and P2 is the sound pressure experienced at the rock concert.

Divide both sides by 20:

Clear the log:

So the sound pressure at a rock concert is 106 or one million times greater than that of the threshold of human hearing.