Halliday, Resnick & Walker — Waves-II: Problem 60

60 Underwater illusion. One clue used by your brain to determine the direction of a source of sound is the time delay $\Delta t$ between the arrival of the sound at the ear closer to the source and the arrival at the farther ear. Assume that the source is distant so that a wavefront from it is approximately planar when it reaches you, and let $D$ represent the separation between your ears. (a) If the source is located at angle $\theta$ in front of you (Fig. 17-36), what is $\Delta t$ in terms of $D$ and the speed of sound $v$ in air? (b) If you are submerged in water and the sound source is directly to your right, what is $\Delta t$ in terms of $D$ and the speed of sound $v_w$ in water? (c) Based on the time-delay clue, your brain interprets the submerged sound to arrive at an angle $\theta$ from the forward direction. Evaluate $\theta$ for fresh water at 20°C.