Question

A source emits sound uniformly in all m)? directions. A radial line is drawn from this source. On this line, determine the radial positions of two points, 0.990 m apart, such at one point is 2.09 dB greater than that at the other. (a) What is the smaller radial position (in m)? (b) What is the larger radial position (in Sound

Answer 1

Let Intensity at point A be I, and Intensity at point B be I_2 rightarrow By Relation of Intensity and distance I alpha 1/s^2 therefore I_1/I_2 = s^2_2/s^2_1 Intensity, level at point A d B_1 = 10 log I_1/I_0 I_1 = Intensity at point, A w/m^2 I_0 = Reference intensity, w/m^2 Similarly Intensity level at point B d B_2 = 10 log I_2/I_0 d B_1 = d B_2 = 10 log I_1/I_0 - 10 log I_2/I_0 2.09 d B = 10 log I_1/I_2 2.09 = 10 log (s_2/s_1)^2 2.09 = 20 log r_2/r_1 log r_2/r_1 = (10)^0.1045 r_2/r_1 = 1.272 equation (i) \r\n and r_2 - r_1 = 0.990 equation (ii) 1.272 r_1 - r_1 = 0.990 r_1 = 0.990/0.272 r_1 = 3.639 m rightarrow smaller Radial position r_2 = 1.272 r_1 r_2 = 1.272 times 3.639 r_2 = 4.629 m rightarrow larger Radial position