Beam divergence is a function of the dimensions of the crystal and the wavelength of the beam transmitted through a medium and it:

Beam divergence is a function of the dimensions of the crystal and the wavelength of the beam transmitted through a medium and it:

• A. Increases if the frequency or crystal diameter is decreased
• B. Decreases if the frequency or crystal diameter is decreased
• C. Increases if the frequency is increased and crystal diameter is decreased
• D. Decreases if the frequency is increased and crystal diameter is decreased

Answer: (A)

Beam divergence comes from diffraction at the finite aperture of the transmitting crystal. A simple way to think about it is that the spread of the beam is proportional to the wavelength divided by the aperture diameter: θ ≈ λ / D. So, if the wavelength gets larger or the aperture (crystal diameter) gets smaller, the beam spreads out more. In a medium, decreasing the frequency increases the wavelength (since λ ∝ 1/f for a given wave speed). That larger wavelength leads to a larger divergence. Similarly, reducing the crystal diameter reduces D, which also increases divergence. So the divergence grows when either the frequency is decreased or the crystal diameter is decreased. On the other hand, increasing frequency (smaller wavelength) or increasing the crystal diameter would reduce divergence, which is the opposite effect. This explains why the option stating that divergence increases with decreased frequency or decreased crystal diameter matches the underlying diffraction behavior. The trade-off with higher frequency is better resolution but more attenuation, which is a practical consideration in ultrasound.

Beam divergence comes from diffraction at the finite aperture of the transmitting crystal. A simple way to think about it is that the spread of the beam is proportional to the wavelength divided by the aperture diameter: θ ≈ λ / D. So, if the wavelength gets larger or the aperture (crystal diameter) gets smaller, the beam spreads out more.

In a medium, decreasing the frequency increases the wavelength (since λ ∝ 1/f for a given wave speed). That larger wavelength leads to a larger divergence. Similarly, reducing the crystal diameter reduces D, which also increases divergence. So the divergence grows when either the frequency is decreased or the crystal diameter is decreased.

On the other hand, increasing frequency (smaller wavelength) or increasing the crystal diameter would reduce divergence, which is the opposite effect. This explains why the option stating that divergence increases with decreased frequency or decreased crystal diameter matches the underlying diffraction behavior. The trade-off with higher frequency is better resolution but more attenuation, which is a practical consideration in ultrasound.