What is the diameter of the baby's head based on ultrasound echoes?

[Boogeyman]

Homework Statement

Ultrasound waves are used to find the size of an unborn baby's head. Echoes are received from the front and the back of the skull bone. The reflected sound pulses are detected and displayed on an oscilloscope screen that shows that the echoes are 0.15ms apart. If the speed of the ultrasound waves through the baby's head is 1400m/s, calculate the diameter of the bay's head. Remember that reflected waves travel twice the distance.

Homework Equations

v=f$$\lambda$$
speed=distance/time

The Attempt at a Solution

So when they say that the echoes are 0.15ms apart, does this mean on the baby's 2 sides of the skull or is it the wavelength of the ultrasound?

1400=f$$\lambda$$

what's the wavelength, and are we supposed to assume frequency is 6.0x10^4Hz?

so this is where I'm stumped. I'm obviously very wrong, i Know.$$\lambda$$

 

[dynamicsolo]

You don't need the wavelength or frequency of the ultrasound waves; they have (essentially) no effect on the travel time of the waves.

The reflected wave from the near side of the skull takes a certain time to make the trip out and back; call that amount of time T. (We don't need to know the value.) The reflected wave takes a longer amount of time T + 0.15 millisecond to reach the far side of the skull and return to the detector. That is what is meant by the difference in the times for the echo returns.

So the difference in those times is basically the added time it takes an ultrasound wave to pass from the near side of the skull to the far side, and back again. How fast does the wave travel? How far does it get in this time interval? How does that distance relate to the size of the fetus' skull?

 

[Boogeyman]

Ok, so the baby's head is in profile right? Since speed=distance/time:

1400=distance/0.15
distance=1400 x (0.15 x 10^-3)=0.21m

Um so is this where you are pointing at?

 

[dynamicsolo]

Ok, so the baby's head is in profile right? Since speed=distance/time:

1400 m/sec = distance/0.15 x 10^-3 sec
distance=1400 x (0.15 x 10^-3)=0.21m

Um so is this where you are pointing at?

Well, we aren't really told which way the waves are being sent through the fetus' skull (the data is probably made up, anyway). But what you have is what the problem is asking for: the difference in the echo times is due to the difference in ultrasound travel time between the reflections from the front and back of the skull.

One more thing, though (and this is mentioned in the last sentence): the ultrasound passing through the skull and returning makes a round trip in 0.15 milliseconds. So how many times has it traveled the diameter of the skull?