Curricular Resources > 1983 Volume VII > Unit 5 (83.07.05) > Section 2

Medical Imaging

CONTENTS OF CURRICULUM UNIT 83.07.05

Unit Guide

The Basic Concepts of Diagnostic Ultrasound1

Beverly Stern

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II. A Little Math Here and There

A. Waves . . . Waves . . . Waves

The following six characteristics hold for all waves whether they are water, sound, light or radio waves.

frequency	propagation speed
period	amplitude
wavelength	intensity

1. Using your notes or the text, write a definition of each of the above wave characteristics.
2. Draw and label illustrations of frequency, period, wavelength and amplitude.
3. Complete the following table.

FREQUENCY PERIOD WAVELENGTH PROPAGATION SPEED

a. 5Hz ——— ——— 800 m/s

b. ——— 0.05 s 1200 ft———

B. Distance = Rate x Time (Distance Formula)

Rate is a ratio, a comparison of two numbers. It means so many of something per so many of something else. Look carefully at the following rate examples.

Rate	Example of Meaning
miles	That car is traveling 55 miles per hour. hour

meters

second	In air sound travels 331 meters per second.
miles	Light travels at 186,300 miles per second. second

For each of these we usually let the second number be 1 of whatever it is: miles per 1 hour, feet per 1 second, meters per 1 second, etc. It doesn’t have to be 1, we could say 331 meters per second or 2648 meters per 8 seconds, and mathematically it work out the same. We use the unit rate to make our work easier.

Use the distance formula and solve the following.

Label each answer.

1. A car traveled 60 miles per hour or 3 hours. How far did it travel?
2. At 42 miles hour for 7.5 hours, how far did it travel?
3. At 45 miles hour for 8 hours, how far did it travel?

In air sound travels 1,100 feet per second.

4. How far will it travel in 4 seconds?
5. How far will it travel in 8 seconds?
6. how far will it travel in 0.3 seconds?

In air sound travels 331 meters per second (m/s).

7. How far will it travel in 7 seconds?
8. How far will it travel in 0.1 seconds?
9. How far will it travel in 4.2 seconds?

In water sound travels 4,800 feet per second (ft/s).

10. How far will it travel in 6 seconds?
11. How far will it travel in 0.2 seconds?
12. How far will it travel in 0.01 seconds?

In water sound travels 1540 meters per second (m/s).

13. In 8 seconds, how far will it go?
14. In 0.5 seconds, how far will it go?
15. In 0,03 seconds, how far will it go?

In soft body tissue sound travels 1540 meters per second.

16. How far will it travel in 1 second?
17. How far will it travel in 0.01 seconds?
18. How far will it travel in 0.000001 seconds?

In soft body tissue sound travels 1.54 millimeters per microsecond.

19. How far will it travel in 3 microseconds?
20. How far will it travel in 8 microseconds?
21. How far will it travel in 24.3 microseconds?

C. Special Problems

Use the following data to solve the given problems.

d = r x t
velocity of sound in air
____ 1,100 ft/s
____ 331 m/s
Velocity of sound in water
____ 4,800 ft s
____ 1,540 m s
velocity of sound in soft body tissue 1540 m/s
____ 1.54 mm/ s
____ 1 mile = 5280uft
1. What is the distance across a canyon if it takes 1 second for your echo to return?Use feet.
2. What is the distance across a canyon it it takes 2.4 seconds for your echo to return? Use feet.
3. If you saw lightning flash 15 seconds before you heard the first rumble of thunder, how far away would the lightning be? Round to nearest mile.
4. If you saw the lightning and 10 seconds later heard the first rumblings of thunder, how far away would the lightning be? Round to nearest mile.
5. You are on a sailing vessel and it takes 3 seconds for an ultrasound pulse to reach the bottom and return. How deep is the water? Give answer in feet and meters.
6. Still at sea, it takes 0.5 seconds for your sound pulse to return. How deep is the water? Give answers in both feet and meters.
7. If it took 0.003 seconds for your sound pulse to return , how deep would the water be? Give answer in both feet and meters.
8. How long would it take an ultrasound echo to return to a ship it the water were 75 feet deep? if water were 15ft. deep?

Use 1.54 millimeters/microseconds for #9and #10.

9. How far into the body would sound travel in 4µs?
10. How far into the body would sound travel in 6.47µs?

D. Bet You Can’t

Using the data in the table on acoustic impedance, can you use this formula (figure available in print form) R=percent of beam reflected

Z1= acoustic impedance of medium 1

Z2= acoustic impedance of medium 2

to find the percentage of beam reflected back at each of these interfaces.

a. chest(soft tissue)—lung(air)

b. kidney—fat

Math Answers

A. Waves . . . Waves . . . Waves

1. use text 2. use text

3a. 5Hz 0.2s 160m 800m/s

3b. 20Hz 0. 1,200ft 24,000ft/s

B. Distance = Rate x Time

1) 180miles 2) 390miles 3) 360 miles 4) 4,400ft

5) 8,800ft 6) 330ft 7) 2317m 8) 33.1ft

9) 1,390.2m 10) 28,800ft 11)960ft 12) 48ft

13) 12,320m 14) 770m 15) 46.2m 16) 1540m

17) 15.4m 18) 0.00154m 19) 4.62mm 20) 12.32m

21) 37.422mm

C. Special Problems

1) 550 feet 2 1320 feet

3) 3 miles 4 2 miles

5) 7,200 feet 6) 1200 feet, 385 meters

7) 7.2 feet, 2.31 meters 8) 0.015625 seconds; 0.003125 seconds

9) 6.16 millimeters 10) 9.96 millimeters

D. Bet You Can’t

1) 99.9% 2) 30%

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	a. 5Hz ———	———	800 m/s
	b. ———	0.05 s	1200 ft———

1. use text	2. use text
3a. 5Hz	0.2s	160m	800m/s
3b. 20Hz	0.	1,200ft	24,000ft/s

1) 180miles	2) 390miles	3) 360 miles	4) 4,400ft
5) 8,800ft	6) 330ft	7) 2317m	8) 33.1ft
9) 1,390.2m	10) 28,800ft	11)960ft	12) 48ft
13) 12,320m	14) 770m	15) 46.2m	16) 1540m
17) 15.4m	18) 0.00154m	19) 4.62mm	20) 12.32m
21) 37.422mm

	1) 550 feet	2 1320 feet
	3) 3 miles	4 2 miles
	5) 7,200 feet	6) 1200 feet, 385 meters
	7) 7.2 feet, 2.31 meters	8) 0.015625 seconds; 0.003125 seconds
	9) 6.16 millimeters	10) 9.96 millimeters