1. What we will do today:
Carry out calculations involving ultrasound

2. How can ultrasound be used to measure the depth of the sea?

3. the ultrasound waves are sent down from a transmitter on the ship . . .
the reflected waves return to the ship where they are picked up by a receiver . . .
. . . but what information do we need to be able to work out the depth of the water?
the waves hit the sea bed and reflect from it as an echo

4. Calculate the depth of the water?
speed of sound in water = 1500 m/s
time taken to reach the sea bed and reflect back to the ship = 0.4 s
. . . but we need something else if we want to work out the depth
we need the equation !
distance d = v x t
d = 1500 x 0.4
d = 600 m
so depth = 300 m
(that’s 300 m down and then m back up again - a total of 600 m)
d = v x t

5. How can ultrasound be used to scan an unborn baby inside the mother?

6. the monitor
the transceiver
the patient !
an ultrasound scanner

7. the ultrasound scanner
. . . and how it works

8. the ultrasound waves travel into the womb from the scanner and reflect from the baby but what information do we need to be able to work out how long it would take to travel to the baby’s head and back again ?

9. How long would the ultrasound take to travel to the baby’s head and back again ?
speed of sound in soft tissue = 1500 m/s
6 cm 6 cm
distance between the scanner and the head of the baby = 0.06 m (6cm)
. . . and we still need something else if we want to work out the time taken
we need the equation !
d = v x t
0.06 = 1500 x t
t = 0.06/1500
t = s
. . . but that is just the time to reach the baby’s head - it will take the same time to reflect back - making a total time of seconds
d= v x t

10. Examples using ultrasound
Take the speed of sound in water and tissue to be 1500 m/s
1. The sonar system on a ship is checked by sending down a pulse of sound to the sea bed at a depth of 200 metres.
Calculate the time taken for the sound to travel to the bottom and back up again.
The time taken for an ultrasound pulse to travel from scanner to baby and back is seconds.
Calculate the distance between the scanner and the baby.
3. Calculate the wavelength of ultrasound waves which have a frequency of 15 MHz.

11. 1.
speed of sound in water = 1500 m/s
Distance to the sea bed = 200m
d = v x t
200 = 1500 x t
t = 200/1500
t = 0.13s
t = 0.13 s
(that’s 0.13s to go down and then 0.13s to come back up again - a total of 0.26 s)

12. 2.
speed of sound in soft tissue = 1500 m/s
Time taken to travel from scanner to baby and back is seconds
How to calculate the distance . . .
time d = v x t
d = 1500 x
d = 0.3 m
. . . but that is distance there and back to the baby’s head – the distance to the baby’s head is 0.15 m

13. 3.
speed of sound in soft tissue = 1500 m/s
an example of the small wavelength used for fine detail = 15MHz
How to calculate the wavelength . . .
v = f x l
l = /
l = m