Final answer:
The wavelength of the ultrasound wave produced by the transducer is 0.6 mm, the axial resolution is 0.3 mm, the lateral resolution is approximately 0.5 mm or less, and the frequency of the ultrasound wave is 10 MHz.
Step-by-step explanation:
To calculate the wavelength (λ), we use the formula:
λ = v / f
Where v is the speed of sound in the medium and f is the frequency.
The speed of sound given is 6 mm/μs (which is equivalent to 6000 m/s), and we want to find the frequency to determine λ.
The frequency (f) can be determined using the thickness (d) of the transducer elements and the speed of sound (v) in the transducer material:
f = v / (2d)
So, f = 6000 m/s / (2 * 0.3 mm) = 10 MHz
Thus, the wavelength (λ) of the ultrasound wave is then:
λ = 6000 m/s / 10×10⁶ Hz = 0.6 mm
The axial resolution is typically approximated as λ/2. Therefore, the axial resolution of the transducer is,
Axial resolution = 0.6 mm / 2 = 0.3 mm
The lateral resolution is affected by the beam width, which is determined by the near field length (NFL), which in turn depends on the diameter (or width) of the transducer element (D) and the frequency (f). The NFL can be estimated with the formula:
NFL = (D² × f) / 4λ
For these calculations, the width of each element is 0.5 mm, and the frequency is 10 MHz.
NFL = (0.5 mm² × 10⁶ Hz) / (4 × 0.6 mm) = 2.08 mm
The frequency of the ultrasound wave is already determined as 10 MHz.
The lateral resolution is approximately the width of the beam in the far field, and we assume that the beam does not diverge significantly within the focal zone where the resolution is measured. Therefore, the lateral resolution would be on the order of the diameter of the transducer elements or smaller, which is 0.5 mm or less in this case.