2. Medical ultrasound machines typically use frequencies
in the range of 2 to 18 MHz
a) What are the corresponding wavelengths in air?
a) Given that the human body contains primarily water
estimate the wavelength range in the body?
Question
3. The relationship between the speed of a sound wave, v, the
frequency, f, and the wavelength, λ, is represented in the
following equation:
v = fλ
The speed of a sound wave depends on the properties of the
medium through which it is propagating.
There is an general trend of of increasing sound speed as we
move from gases to solids.
The speed of sound in air at 20 degrees Celsius is 343 m/s. The
speed of sound in liquid water at 20 degrees Celsius is 1,482
m/s.
Solving the Problem
4. a)
v = 343 m/s
f = 2 MHz = 2,000,000 Hz
= 18 MHz = 18,000,000 Hz
v = fλ v = fλ
λ = v/f λ = v/f
λ = (343 m/s)/(2,000,000 Hz) λ = (343 m/s)(18,000,000)
λ = 1.7e-4 m λ = 1.5e-5 m
The corresponding wavelengths are 1.7e-4 m to 1.5e-5 m
Putting it all Together
5. b)
v = 1,482 m/s
f = 2 MHz = 2,000,000 Hz
= 18 MHz = 18,000,000 Hz
v = fλ v = fλ
λ = v/f λ = v/f
λ = (1,482 m/s)/(2,000,000 Hz) λ = (1,482 m/s)(18,000,000)
λ = 7.4e-4 m λ = 8.2e-5 m
The corresponding wavelengths are 7.4e-4 m to 8.2e-5 m
6. The ultrasound machine transmits high frequency sound pulses into your
body using a probe.
The sound waves travel into you body and hit a boundary between tissues.
Some of the waves get reflected back to the probe, while some travel on
further until they reach another boundary and get reflected.
The reflected waves are picked up by the probe and relayed to the
machine.
The machine calculates the distance from the probe to the boundaries
(tissue or organ) using the speed of sound in tissue and the time of each
echo’s return.
The machine displays the distances and intensities of the echoes on the
screen, forming a two dimensional image.
Further Information on Ultrasounds
