1. Consider a 300 element, linear array transducer, which is 50 mm between the centre lines of the first and the three-hundredth elements. Determine the pitchof the elements, that is to say, the distance between the centre lines of successive elements.
2. At a given time, a single beam is generated by an active group of 19 elements. This beam is steered 11.5 degrees off-axis to the right as measured at the centre of the group to a focal point at a depth of 6.5 cm. Figure 1 (below) is a schematic diagram of this single group showing elements 1 to 19 (not all elements are shown) and the focal point.

(Note that this diagram is not to scale.Diagrams that are not to scale are often used in diagrammatic representations. In this case, the group of elements appears to be much larger than its actual size relative to the 6.5 cm depth dimension which appears much shorter than the actual depth, and the 11.5-degree angle appears much larger than 11.5 degrees.)

State the order in which elements 1, 10 and 19 have to be fired. Then, calling the time at which the first element is fired, time zero, calculate the time at which the other two elements are subsequently fired. The two successive times will be given in ms, ?s, or ns as appropriate.

Hint: You can use knowledge of the element pitch, elementary trigonometry, and the theorem of Pythagoras, to determine the three path lengths from elements 1, 10 and 19 to the focal point and hence, determine the time delays between the firing times of the three elements.

Current element group using elements 1 to 19 (not all elements shown) 1 2 10 18 19 A BI C D 11.5' Element 1 path to focal point 6.5 Figure 1 A single active group of transducer elements with the beam steered 11.5' off axis to the right to the focal point shown. Focal point