# Arrival time from two US transducers

• enc08
In summary, the conversation involves a discussion about T1 and T2 ultrasound transducers and calculating the difference in arrival time at the focal point when a pulse is emitted from both transducers. The speaker is getting a different answer than what is indicated on the answer sheet and is seeking clarification on if their approach of finding the equivalent sound speed is correct. The expert summarizes that the method works in this case because refraction is not taken into account, but if it was, the ratio of times spent in each media may differ.
enc08
Hi,

Please refer to the attached image.

T1 and T2 are ultrasound transducers. The focal point of the transducers is 2cm into the liver tissue.

Q) A pulse is emitted from both transducers at the same time. Calculate the difference in arrival time at the focal point.

I seem to be getting the wrong answer. This is what I'm doing:

The arrival time from T2 is: $$t_{T2} = 1cm/1450 + 2cm/1540 = 19.9us$$

From this we can calculate an equivalent average speed across both tissue:
$$c_{equiv} = 3cm/19.9us = 1508.8m/s$$

Using this we'll calculate the arrival time for T1
$$t_{T1} = \sqrt{(9.6mm)^2 + (3cm)^2}/c_{equiv} = 20.9us$$

Thus the difference in arrival time is $$1us$$
However the answer sheet indicates $$0.4us$$

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Hint: Snell's law

EDIT: On reflection (pun!) I can see that refraction of the sound wave at the fat/liver interface is not going to make a great deal of difference in the result... So perhaps your answer is correct and the given answer is not.

Last edited:
Hi,

Thanks. We aren't expected to consider to reflection in this question.

So my approach of finding the equivalent sound speed is right?

enc08 said:
Hi,

Thanks. We aren't expected to consider to reflection in this question.

So my approach of finding the equivalent sound speed is right?

Sure. The method works because, not considering refraction, the ratio of the times spent in each media is the same for both paths.

If refraction was taken into account and resulted in a different ratio, then this would not be the case.

Thanks.

## 1. What is the arrival time from two US transducers?

The arrival time from two US transducers refers to the time it takes for an ultrasonic signal to travel from one transducer to another. This can be used to measure the distance between the two transducers or to detect the presence of an object.

## 2. How is the arrival time calculated?

The arrival time is calculated by measuring the time it takes for the ultrasonic signal to travel from one transducer to another and back again. This is typically done using a timer or by measuring the frequency of the signal.

## 3. What factors can affect the arrival time from two US transducers?

The arrival time can be affected by various factors including the distance between the transducers, the speed of sound in the medium through which the signal is traveling, and any obstructions or reflections that may alter the path of the signal.

## 4. How accurate is the arrival time from two US transducers?

The accuracy of the arrival time can vary depending on the precision of the equipment and the environmental conditions. Generally, the arrival time can be measured with a high degree of accuracy, but it may be affected by external factors such as temperature and humidity.

## 5. What are the applications of measuring arrival time from two US transducers?

The measurement of arrival time from two US transducers has various applications, including distance measurement in robotics and autonomous vehicles, object detection in security systems, and medical imaging in ultrasound technology. It can also be used in underwater communication and navigation systems.

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