Question

Ultrasonic waves, like all other waves, exhibit diffraction. Recall that the minimum half angle of a beam is given by:
alpha = (1.22*λ_m)/d
The wavelengths used in ultrasound imaging techniques are generally in the range from 0.3 mm to 0.75 mm [longer waves (lower frequencies) penetrate more deeply but provide less resolution of detail than the short waves]. In order for an ultrasonic beam to spread by less than a centimeter after it has traveled across a human torso (20 cm), the source of the waves must be about 10 or 20 times larger than the wavelength. The source of the waves is called a transducer.

Question:

A transducer is 19.5 mm in diameter and emits a wave of wavelength 0.50 mm. The beam travels a total distance of 37 cm through the patient and back to the transducer. How much has the beam spread after returning to the transducer? (Hint: Start with the formula, α = 1.22λ_m /d, and recall that this is the minimum HALF angle of the beam.)

Answer must be in mm.

The answer is NOT 0.0106mm or 0.611mm, these are wrong answers. I will be sure to give a good rating to the person who answers correctly.

Answer 1

Given,

Therefore, the minimum half angle of a beam is given by,

Cover this into degrees. For that multiply using

Therefore,

From the figure the total spread is 2S

From the figure,

Therefore total spread is given by,