(a) Find the size of the smallest detail observable in human...

(a) Find the size of the smallest detail observable in human tissue with 20.0 -MHz ultrasound. (b) Is its effective penetration depth great enough to examine the entire eye (about $3.00 \mathrm{~cm}$ is needed)? (c) What is the wavelength of such ultrasound in $0^{\circ} \mathrm{C}$ air?

Key Concepts

Ultrasound Wavelength and Frequency

This concept involves the relationship between the speed of sound, frequency, and wavelength, expressed by the formula wavelength = speed/frequency. In ultrasound imaging, higher frequencies lead to shorter wavelengths, which in turn allow for finer detail to be resolved. The wavelength in the medium is central to determining both the resolution and the operational characteristics of the ultrasound system.

Resolution in Ultrasound Imaging

Resolution refers to the smallest detail that an imaging system can observe. In ultrasound, the resolution is closely linked to the wavelength of the sound in the tissue—a shorter wavelength typically permits finer spatial resolution. This means that an ultrasound system operating at a higher frequency can generally distinguish smaller structures, although other factors like pulse length and system bandwidth may also affect the effective resolution.

Attenuation and Penetration Depth

Attenuation describes the reduction of ultrasound intensity as it travels through tissue, mainly due to absorption and scattering. Higher frequency ultrasound waves are attenuated more rapidly, which limits their effective penetration depth. This concept highlights the trade-off in ultrasound imaging between the desire for high resolution (via high frequency and short wavelengths) and the need for sufficient tissue penetration to image deeper structures.

Speed of Sound in Different Media

The speed at which sound travels varies between different media, and this variation directly affects the calculation of wavelength. For example, human tissue typically has a higher sound speed compared to air. Understanding these differences is crucial when calculating parameters like wavelength in various contexts, as the properties of the medium (such as temperature in air) must be considered to accurately determine ultrasound characteristics.

Transcript

00:01 So in this problem, we want to get the smallest detail observable with tissue with a 200 megahertz ultrasound.

00:08 So frequency is equal to 200 megahertz.

00:15 So that's 200 times 10 to the 6 hertz.

00:20 And we want to basically get, so the smallest details that can be observed mean that they're on the order of the wavelengths.

00:27 So we want the wavelength.

00:28 And then we also need the velocity that the wave.

00:31 Is going to travel in tissue and the velocity from the table is 1450 meters per second.

00:39 So lambda is going to be velocity meters per second.

00:46 And then we need to divide by a frequency to cancel out the units of seconds.

00:52 Right.

00:52 One over seconds.

00:54 So we can do 1450 divided by 200 times 10 to the 6.

01:02 Divided by, i forgot how i said divided by or multiplied by.

01:05 So 1450 divided by 200 times 10 to the 6, 1, 2, 3, 4, 5, 6.

01:11 So i get 7 .25 times 10 to minus 6 meters.

01:25 So 7 something microns, basically.

01:32 And i can see the answer that somebody else got here and they had 77.

01:36 I think i'm not sure maybe they're using a different speed for the velocity oh it was 20 .0, not 200.

01:46 I thought that seemed a little high frequency so actually let me go revise that so now i go so now i can say 72 .5 times 10 to the minus 5 meters and we want to get the depth can you see the whole eye? and so three centimeters is needed...

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