Final answer:
For an ultrasound study of the thyroid gland, a 10 MHz transducer is typically the most appropriate due to the gland's superficial location and the need for high resolution, which is not an option provided, so the closest highest frequency listed which is 7.5 MHz would be chosen.
Step-by-step explanation:
The choice of frequency for a transducer for ultrasound imaging depends on the balance between image resolution and penetration depth. The frequencies mentioned range from 1 MHz to 10 MHz. In general, higher frequencies such as 10 MHz offer greater resolution but have a shallower penetration depth, while lower frequencies such as 1 MHz or 2.25 MHz have deeper penetration but provide lower resolution. For thyroid gland studies, a medium-frequency transducer is often used to provide a good balance. Therefore, the most appropriate frequency from the options provided would typically be 7.5 to 10 MHz, with the best choice being 10 MHz (not listed as an option in the question but an accepted standard for thyroid ultrasound exams). This is due to the thyroid gland being relatively superficial and requiring higher resolution for adequate detail.
To determine the beat frequency, one would typically need the Doppler shift that occurs when ultrasound is reflected from a moving object, such as blood in a bloodstream. However, since the main question does not provide enough information to calculate a beat frequency, and a 10 MHz transducer would be most appropriate for a thyroid study, such a calculation is not the focus here.