Beam Spread (Approximation)

Understanding Beam Spread

As an ultrasonic wave travels through a material, the sound beam gradually becomes wider. This natural expansion, known as beam spread or beam divergence, affects the area inspected and influences the ability to detect and accurately size discontinuities at different depths.

Beam spread is primarily determined by the probe frequency, active element diameter and the sound velocity of the test material.

This calculator provides an approximate beam profile using the first null approximation, making it ideal for visualising beam behaviour and understanding how probe selection influences inspection coverage.

Why Beam Spread Matters

Understanding beam spread helps technicians:

• Estimate inspection coverage at different depths.
• Select the most suitable probe for an application.
• Determine scan spacing and overlap.
• Improve defect detection probability.
• Understand changes in beam width with increasing sound path.

A beam that is too narrow may miss discontinuities if scan spacing is excessive, while a beam that spreads too quickly may reduce sensitivity at greater depths.

Factors That Affect Beam Spread & Calculation

Probe Frequency
Higher frequency probes produce shorter wavelengths, resulting in a narrower beam with less divergence. Lower frequency probes generate wider beams that spread more rapidly but provide greater penetration.

Probe Diameter
Larger probe elements produce tighter, more focused beams with reduced divergence. Smaller elements generate wider beams and greater beam spread.

Material Properties
Sound velocity changes the wavelength within the material, which directly influences beam divergence. Different materials therefore produce slightly different beam characteristics even when using the same probe.

Calculation Method

The calculator estimates beam spread using the first null approximation, a widely accepted method for illustrating beam behaviour. The following relationships are used:

• Wavelength: λ = v ÷ f
• First Null Half Angle: sin θ = 1.22 λ ÷ D
• Beam Radius: r = L × tan θ

• λ = Wavelength
• v = Sound velocity
• f = Probe frequency
• D = Active element diameter
• θ = Beam divergence half angle
• L = Sound path length
• r = Beam radius