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Ultrasonic Inspection - Beam Spread

A round transducers produces a cylindrical sound field in front of the transducer. However, the energy in the beam does not remain in a cylinder, but instead spread out as it propagates through the material. The phenomenon is usually referred to as beam spread. For more informaiton on beam spread see the NDT On-line material.

Beam spread for a flat piston source transducer is a function of the transducer diameter (D), transducer frequency (F), and the sound velocity (V) in the liquid or solid medium through which the sound is travelling. The equation below can be used to calculate the beam divergence angle (1/2 beam spread angle). This angle represents a measure from the center of the acoustic axis to the point where the sound pressure has decreased by one half (-6 dB) to the side of the acoustic axis.

Where: q = Beam spread angle from acoustic centerline to point where signal is at half strength.
  V = Sound velocity in the material being evaluated.
  D = Diameter of the transducer.
  F = Frequency of the transducer.

Example Calculation

Calculate the beam spread when using a 2.25 MHz, 0.375 inch diameter transducer to inspect a component made of brass. The sound velocity in brass is 0.1685x106 inch/second

Substitute the values into the formula.     

Cancel terms where possible.

        

Simplify.

Multiply and divide.

With a calculator find the inverse sin (sin-1) of 0.2396.

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The beam divergency is 13.86 degrees so beam spread, which is 2 times the beam divergency, will be approximately 27.7 degrees.