How does increasing the wavelength affect the half-angle beam divergence in the quartz crystal formula when diameter is fixed?

• A. It becomes zero
• B. It decreases
• C. It increases
• D. It remains the same

Answer: (C)

Beam divergence in ultrasonics comes from diffraction at the transducer’s finite aperture. For a circular transducer with diameter D, the half-angle of the main beam is roughly proportional to λ/D (for example, θ ≈ 0.61 λ/D for the first null). With the diameter fixed, increasing the wavelength λ increases the ratio λ/D, so the half-angle beam divergence becomes larger. In other words, longer wavelengths diffract more and the beam becomes less focused. So the correct effect of increasing wavelength at fixed diameter is that the half-angle beam divergence increases.