To determine which transition results in the largest change in the wavelength of the ultrasound wave, we need to consider the relationship between speed, frequency, and wavelength. The speed of the wave (v), frequency (f), and wavelength (λ) are related by the equation:
\[ v = f \cdot \lambda \]
When an ultrasound wave transitions from one tissue to another, its frequency remains constant, while its speed changes. This leads to a change in wavelength according to the formula:
\[ \lambda = \frac{v}{f} \]
When the speed changes significantly, the corresponding wavelength changes significantly as well.
Let's analyze the transitions provided:
-
Fat to Liver
- Speed change: 1,450 m/s to 1,550 m/s
- Change in speed: \(1,550 - 1,450 = 100 , \text{m/s}\)
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Liver to Muscle
- Speed change: 1,550 m/s to 1,580 m/s
- Change in speed: \(1,580 - 1,550 = 30 , \text{m/s}\)
-
Muscle to Kidney
- Speed change: 1,580 m/s to 1,560 m/s
- Change in speed: \(1,560 - 1,580 = -20 , \text{m/s}\)
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Blood to Fat
- Speed change: 1,570 m/s to 1,450 m/s
- Change in speed: \(1,450 - 1,570 = -120 , \text{m/s}\)
Now, calculate the absolute changes in speed:
- Fat to Liver: 100 m/s
- Liver to Muscle: 30 m/s
- Muscle to Kidney: 20 m/s
- Blood to Fat: 120 m/s
The largest absolute change in speed occurs in the transition Blood to Fat with a change of 120 m/s. As such, this will result in the largest change in wavelength.
Thus, the answer is:
Blood to Fat