Question

a medical technician uses an ultrasound machine to scan a patients heart. the technician adjusts the machine to a higher frequency. what effect will this adjustment most likely have on the image? the image will display less diffraction at the edges of internal organs. the image will display sharper details of the heart but with less depth. the image will display deeper organs but with reduced sharpness. the image will display more absorption by bones in the body.

Explanation:

• For the relationship between frequency and wavelength: The formula \(v = f\lambda\) (where \(v\) is the speed of sound in the medium, \(f\) is the frequency, and \(\lambda\) is the wavelength) is relevant. In a given medium (e.g., human tissue), the speed of sound \(v\) is approximately constant. So, when \(f\) increases, \(\lambda\) decreases (\(\lambda=\frac{v}{f}\)).
• For image sharpness and depth:
• Sharpness: Shorter wavelengths (\(\lambda\)) lead to better resolution (sharper details). This is because they can more accurately reflect off small structures.
• Depth: The penetration depth \(d\) of ultrasound in tissue is related to the attenuation coefficient \(\alpha\) and the wavelength \(\lambda\). Higher - frequency (shorter - wavelength) ultrasound is more attenuated (absorbed) in tissue. The attenuation formula for soft tissue is approximately \(I = I_0e^{-\alpha x}\), where \(\alpha\) is larger for higher - frequency ultrasound. So, higher - frequency ultrasound has less penetration depth.
• For diffraction: Diffraction \(D\) is related to the wavelength \(\lambda\) and the size of the object \(a\) (\(D\propto\frac{\lambda}{a}\)). A decrease in \(\lambda\) (due to higher \(f\)) would decrease diffraction, but this is not the main factor affecting the trade - off between sharpness and depth in medical ultrasound imaging.
• For bone absorption: While bone does absorb ultrasound, the main effect of changing the frequency (in the context of the question about the image) is the trade - off between sharpness and depth, not primarily related to bone absorption compared to the sharpness - depth relationship.

Answer:

The image will display sharper details of the heart but with less depth.