I was not exactly sure how to relate the Ultrasound to a Ulnar Collateral Ligament Physics problem.  Therefore, to show you that I understand the physics behind an Ultrasound problem I created a different situation for my quantitative data.

Ultrasound is used in medicine both for diagnostic imaging and for therapy. For diagnosis, short pulses of ultrasound are passed through the patient's body. An echo reflected from a structure of interest is recorded, and from the time interval for the return of the echo the distance to the structure can be determined. A single transducer emits and detects the ultrasound. An image of the structure is obtained by reducing the data with a computer. With sound of low intensity, this technique is noninvasive and harmless. It is used to examine fetuses, tumors, aneurysms, gallstones, hearts, and many other structures. To reveal details, the wavelength of the reflected ultrasound must be small compared with the size of the object reflecting the wave.

A- What is the wavelength of ultrasound with a frequency of 2.4 MHz, used in echo cardiography to map the beating heart?

For this Problem you can simply use Speed= Frequency x wavelength

Given

Speed=1500m/s

Frequency= 2.4 Hz

Wavelength= ?

1500m/s=(2.4x10^6)(?)

1500m/s/(2.4x10^6Hz)=?

Wavelength (l)= 6.25x10^-4

Wavelength(l)= 625x10^-6m or 625 microns

B- In the whole set of imaging techniques, frequencies in the range of 1.00 to 20.0 MHz are used. What is the range of wavelengths corresponding to this range of frequencies? The speed of ultrasound in human tissue is about 1500 m/s (nearly the same as the speed of sound in water).

(b) Frequency= 1.0 MHz

1500m/s = (1.0 x 10^6 )(wavelength)

1500 m/s/ (1.0 *x10^6 ) = wavelength

1500 m/s* (10^-6 m) = wavelength

l=1500 microns

wavelength=1.5 nm

Frequency= 20 MHz

1500 = 20.0 * 10^6(wavelength)

1500 / (20.0 * 10^6 ) =wavelength

75 * 10^-6 m = wavelength

wavelength=75 microns

wavelength=0.075 nm

Range= 0.075nm to 1.5nm