To determine which transition results in the largest change in the wavelength of the ultrasound wave, we first need to understand that the wavelength (\( \lambda \)) of a wave is inversely proportional to its speed (\( v \)) in a medium, according to the formula:
\[ \lambda = \frac{v}{f} \]
where \( f \) is the frequency of the wave. Since the frequency remains constant when the wave travels from one medium to another, any change in speed will lead to a change in wavelength.
The changes in wavelength can be inferred from the change in speed when moving from one tissue to another. Looking at the speed values for the given tissues:
- Muscle: 1,580 m/s
- Kidney: 1,560 m/s
- Liver: 1,550 m/s
- Blood: 1,570 m/s
- Fat: 1,450 m/s
Now let's analyze the options:
-
Muscle to Kidney:
- Speed changes from 1,580 m/s to 1,560 m/s
- Change in speed = 1,560 - 1,580 = -20 m/s
-
Liver to Muscle:
- Speed changes from 1,550 m/s to 1,580 m/s
- Change in speed = 1,580 - 1,550 = 30 m/s
-
Blood to Fat:
- Speed changes from 1,570 m/s to 1,450 m/s
- Change in speed = 1,450 - 1,570 = -120 m/s
-
Fat to Liver:
- Speed changes from 1,450 m/s to 1,550 m/s
- Change in speed = 1,550 - 1,450 = 100 m/s
Now, let's summarize the absolute changes:
- Muscle to Kidney: 20 m/s
- Liver to Muscle: 30 m/s
- Blood to Fat: 120 m/s (largest change)
- Fat to Liver: 100 m/s
The largest absolute change in speed occurs during the transition from Blood to Fat, which results in a significant change in wavelength.
Thus, the correct answer is: blood to fat.