To determine which transition results in the largest change in wavelength when an ultrasound wave moves between different tissues, we need to consider the speed of sound in each of those tissues and how it relates to wavelength. The wavelength (\( \lambda \)) of a wave is given by the formula:
\[ \lambda = \frac{v}{f} \]
where \( v \) is the speed of sound in the medium, and \( f \) is the frequency of the ultrasound wave, which remains constant when transitioning from one medium to another.
Since the frequency is constant, the change in wavelength is directly related to the change in speed of the ultrasound wave in different tissues. Thus, we should identify which transition has the largest difference in speed.
Here are the transitions to consider:
-
Fat to Liver:
- Speed in Fat: 1,450 m/s
- Speed in Liver: 1,550 m/s
- Change: |1,550 - 1,450| = 100 m/s
-
Blood to Fat:
- Speed in Blood: 1,570 m/s
- Speed in Fat: 1,450 m/s
- Change: |1,570 - 1,450| = 120 m/s
-
Liver to Muscle:
- Speed in Liver: 1,550 m/s
- Speed in Muscle: 1,580 m/s
- Change: |1,580 - 1,550| = 30 m/s
-
Muscle to Kidney:
- Speed in Muscle: 1,580 m/s
- Speed in Kidney: 1,560 m/s
- Change: |1,560 - 1,580| = 20 m/s
Now, comparing the changes in speed for all transitions:
- Fat to Liver: 100 m/s
- Blood to Fat: 120 m/s
- Liver to Muscle: 30 m/s
- Muscle to Kidney: 20 m/s
The transition from blood to fat results in the largest change in speed, which would consequently result in the largest change in wavelength.
Therefore, the correct response is:
blood to fat