Calculate the diameter of a baby's head using ultrasound speed

[Littlegirloud]

Homework Statement

Calculate the diameter of a baby's head if there is a time delay of 96 microseconds between receiving pluses from either side of the skull and the speed of ultrasound can be assumed to be 1250m/s.

Homework Equations

The Attempt at a Solution

The diameter of the baby’s head can be calculated using distance = speed x time where:

Speed of ultrasound = 1250 m/s
= 0.00125 m/ms

Therefore:
Distance (diameter) = 0.00125 x 96
=0.08625 m
= 8.6 cm (1dp)

Where am in going wrong? I'm advised to think about the echo factor the sound waves leaves the transducer reaches the skull and then has to travel back to the transducer.

Please help!

 

[mfb]

Distance (diameter) = 0.00125 x 96
=0.08625 m

I get a different result in that multiplication.

There is another error. Imagine the source of the sound is directly at one side of the head of the baby. In terms of "head diameters", how far does the sound travel to reach the opposite side of the head and come back?

 

[Littlegirloud]

Thanks for the pointer on the calculation, I'll do it again. Is the second mistake that I'm only considering travel time in one direction? So 96x2 to a count for return time too? For some reason I'm just really struggling to get my head around (pun half intended) this one.

 

[mfb]

So 96x2 to a count for return time too?

That is the wrong direction.
The sound needs 96 microseconds for both directions together.

 

[Littlegirloud]

Thank you!

 

[Littlegirloud]

Here's my updated attempt. Closer?

The diameter of the baby’s head can be calculated using distance = speed x time where:
Speed of ultrasound = 1250 m/s
= 0.00125 m/ms

and if 96 microseconds is the time taken for the wave to reflect then time taken across the baby’s head = 96/2
= 48

Therefore:
Distance (diameter) = 0.00125 x 48
= 0.06 m
= 6 cm

 

[haruspex]

Here's my updated attempt. Closer?

The diameter of the baby’s head can be calculated using distance = speed x time where:
Speed of ultrasound = 1250 m/s
= 0.00125 m/ms

and if 96 microseconds is the time taken for the wave to reflect then time taken across the baby’s head = 96/2
= 48

Therefore:
Distance (diameter) = 0.00125 x 48
= 0.06 m
= 6 cm

Yes, but "ms" is the abbreviation for milliseconds. For microseconds it is μs.