Question no 1

(b) When describing an acoustic eld, there are various metrological quantities commonly quoted in addition to the acoustic pressure. One example is the quantity fsata. (i) What does the subscript sofa stand for? (ii) Suppose a focused single element transducer emits a series of acoustic pulses, and the resulting acoustic eld is measured, ie. a set of acoustic pressure time series are measured on a suitable grid of points in front of the transducer. Describe the steps that would need to be taken to determine the value of fsata for this set of measurements. (iii) What would be a 'suitable grid' for measurements such as these?l (c) Usually, the acoustic wave equation is written for the acoustic pressure. Using Eqs. (3) and the linear pressure-density relation, and assuming both the sound speed 60(1) and mass density pa (3:) are spatially-varying, derive the following equation describing the acoustic density uctuations p: 62p E = pas - (private) (4} \f(iv)Using the pressure-density relation derived in part (iii), or otherwise, show that the nonlinearity described by Eq. (5} changes the wave speed by a factor 1 + . (T) (v) Using the linear pressure-density relation, calculate the acoustic density uctuation. (vi}Assuming the nonlinearity parameter is 5 and the acoustic pressure amplitude is lOMPa, calculate the nonlinear factors for the acoustic pressure and for the wave speed. (vii) Comment on whether these factors and numerically similar and why