Question

Which formula is correct in regards to the relationship between frequency of a transducer, thickness of the element, and speed of sound

A. Frequency (MHz) = sound's speed in PZT (mm/µs)/ 2 X thickness of the PZT (mm)
B. Frequency (MHz) = sound's speed in PZT (mm/µs) X thickness of the PZT (mm)
C. Frequency (MHz) = sound's speed in PZT (mm/µs)/thickness of the PZT (mm)
D. Frequency (Hz) = sound's speed in PZT (mm/µs)/2 X thickness of the PZT (mm)
E. Frequency (MHz) = sound's speed in PZT (m/s)/ 2 X thickness of the PZT (mm).

Answer 1

The correct relationship between frequency, the transducer's element thickness, and speed of sound is described by the formula: Frequency = sound's speed in PZT / (2 x thickness of PZT). It expresses that frequency is inversely proportional to wavelength and hence to the thickness of the transducer element for a constant speed of sound.

Step-by-step explanation:

The correct formula that describes the relationship between the frequency of a transducer, the thickness of the element, and the speed of sound is given by option A: Frequency (MHz) = sound's speed in PZT (mm/\u00b5s) / 2 X thickness of the PZT (mm). The formula is based on the understanding that the frequency of a wave is inversely proportional to its wavelength in a given medium, and for a fixed speed of sound, the frequency multiplied by the wavelength is a constant. Thus, a thinner transducer element, which is equivalent to a shorter wavelength, will produce a higher frequency given a constant speed of sound.