18
Level 1
Basic Ultrasound Physics
What Determines the Wavelength
The wavelength changes with changes in the frequency of the wave
and with changes in the propagation velocity of the wave. In other
words,the wavelength depends on characteristics of both the source
and the medium. The illustrations of
Figure 20
and
Figure 21
dem-
onstrate how the wavelength varies with change in the frequency of
the wave, and with change to the propagation velocity of the wave.
Fig. 20
Wavelength dependence on propagation velocity
Scenario 1:
Referring to
Figure 20
, waves A and B are both the same frequency
since both waves have 2 cycles per second (2 Hz). However, wave B
travels a greater distance than wave A during 1 second, so medium
B has a higher propagation velocity than medium A. From
Figure
20
, it is clear that wave B also has a longer wavelength. Therefore, as
the propagation velocity increases,the wavelength also increases,or
mathematically we can say that the wavelength and the propagation
velocity are proportional:
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Scenario 2:
Referring to
Figure 21
, waves A and B are in the same medium
and hence, have the same propagation velocity. However, wave A
has three cycles per second, whereas wave B has only two cycles
per second. Wave A represents a higher frequency wave than wave
B. From
Figure 21
, it is clear that wave B has a longer wavelength.
Therefore, as the frequency decreases, the wavelength increases, or
mathematically we can say that the wavelength and the frequency
are inversely proportional:
Fig. 21
Wavelength dependence on frequency
KEY CONCEPT
The Wavelength Equation
The two relative expressions just derived can be combined into one
equation, or:
This equation is referred to,not surprisingly,as the wavelength equa-
tion. Because of its importance in diagnostic ultrasound, we will
be reviewing the wavelength equation in more depth in Level 2 and
then persistently throughout the rest of this text. You must commit
this equation to memory.
Different Ways of Remembering the Wavelength Equation
Beside brute force memorization, there are at least two other means
by which you can recall the all important wavelength equation. The
first of these two approaches is to go through the mental thought
experiments just discussed. This approach is very useful since it
forces you to think about the physical relationships between the
wavelength and the frequency and between the wavelength and the
propagation velocity.
The other approach is to use the units to help you recall the equa-
tion. Consider the units for frequency, propagation velocity, and
wavelength:
Frequency (f)
•
Wavelength (
λ
)
=
Propagation Velocity (c)
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