Attenuation of Sound Waves

When 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 and absorption. 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 2.71828.

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 equation.

Where v is the velocity of sound in meters per second and Ut is in decibels per second.