of Sound Waves
sound travels through a medium, its intensity diminishes with
distance. In idealized materials, sound pressure (signal amplitude)
is only reduced by the spreading of the wave. Natural materials,
however, all produce an effect which further weakens the sound.
This further weakening results from scattering
Scattering is the reflection of the sound in directions other than its original direction of propagation. Absorption is the conversion of the sound energy to other forms of energy. The combined effect of scattering and absorption is called attenuation. Ultrasonic attenuation is the decay rate of the wave as it propagates through material.
Attenuation of sound within a material itself is often not of
intrinsic interest. However, natural properties and loading conditions
can be related to attenuation. Attenuation often serves as a measurement
tool that leads to the formation of theories to explain physical
or chemical phenomenon that decreases the ultrasonic intensity.
The amplitude change of a decaying plane
wave can be expressed as:
In this expression A0
is the unattenuated amplitude of the propagating wave at some location. The
amplitude A is the reduced amplitude
after the wave has traveled a distance z
from that initial location. The quantity
is the attenuation coefficient of the wave traveling in the z-direction.
The dimensions of are
nepers/length, where a neper is a dimensionless quantity. The term e
is the exponential (or Napier's constant) which is equal to approximately
The units of the attenuation value in Nepers per meter (Np/m) can be converted
to decibels/length by dividing by 0.1151. Decibels is a more common
unit when relating the amplitudes of two signals.
Attenuation is generally proportional to the square of sound
frequency. Quoted values of attenuation are often given for a
single frequency, or an attenuation value averaged over many frequencies
may be given. Also, the actual value of the attenuation coefficient
for a given material is highly dependent on the way in which the
material was manufactured. Thus, quoted values of attenuation
only give a rough indication of the attenuation and should not
be automatically trusted. Generally, a reliable value of attenuation
can only be obtained by determining the attenuation experimentally
for the particular material being used.
Attenuation can be determined by evaluating the multiple backwall
reflections seen in a typical A-scan display like the one shown
in the image at the top of the page. The number of decibels between two adjacent
signals is measured and this value is divided by the time interval
between them. This calculation produces a attenuation coefficient
in decibels per unit time Ut.
This value can be converted to nepers/length by the following
Where v is the velocity
of sound in meters per second and Ut
is in decibels per second.