Final answer:
The minimum frequency of ultrasound to see details of 0.250 mm in human tissue is slightly above 6.16 MHz, making 10.0 MHz the closest standard higher frequency that fits the requirement. The frequency determines the maximum resolution, but higher frequencies have shallower penetration depths.
Step-by-step explanation:
To calculate the minimum frequency of ultrasound required to observe details in human tissue, we can use the relationship between wavelength, frequency, and the speed of sound within the tissue. The speed of sound in human tissue is approximately 1540 m/s. According to the information provided, using higher frequencies allows for greater detail but reduces penetration depth, and 7 MHz ultrasound provides a wavelength of 0.22 mm in tissue, which is sufficient for most purposes. However, to see details as small as 0.250 mm, we would need a frequency that produces a smaller wavelength.
We can use the formula λ = v / f, where λ is the wavelength, v is the speed of sound in the tissue, and f is the frequency. To resolve details of 0.250 mm, we need λ ≤ 0.250 mm or 0.250 x 10⁻³ meters. Thus:
f ≥ v / λ
f ≥ 1540 m/s / (0.250 x 10⁻³ m)
f ≥ 6.16 x 10¶ Hz or 6.16 MHz
Therefore, the minimum frequency to see details of 0.250 mm in tissue is slightly above 6.16 MHz, and the closest higher standard frequency option provided is 10.0 MHz.
However, when it comes to effective depth, higher frequencies have a shallower penetration depth. The 'rule of thumb' for ultrasound depth is about 500 times the wavelength in tissue. Hence, for a 10.0 MHz frequency with a smaller wavelength, the depth would be less compared to lower frequencies.