A transducer with the velocity of a cheetah

Is your ultrasonic transducer faster than a cheetah? Of course your ultrasonic transducer doesn't run across land, as a resonating device it oscillates about a reference point. However, if we back calculate the displacement of a transducer oscillating at the speed of a cheetah, assuming the transducer is working at a classic 40 kHz, here is what we get:

Velocity = Displacement * 2 pi * frequency

That give a displacement of 115 um.

An amazing acceleration

The displacement of ultrasonic transducers are puny, but the velocity is formidable. However, the acceleration is AMAZING!

Acceleration = Velocity * 2 pi * frequency

Acceleration = 7,288,495 m/s^2

A cheetah can reach a speed of 100 kph in three seconds, which is an acceleration of 9.25 m/s^2. 

Therefore, the acceleration of the transducer is ~800,000 times larger than that of a cheetah. WOW! This high frequency acceleration is the cause of large localized forces in many transducer applications.