Halliday, Resnick & Walker — Waves-I: Problem 46

46 A sand scorpion can detect the motion of a nearby beetle (its prey) by the waves the motion sends along the sand surface (Fig. 16-35). The waves are of two types: transverse waves traveling at \( v_t = 50 \text{ m/s} \) and longitudinal waves traveling at \( v_l = 150 \text{ m/s} \). If a sudden motion sends out such waves, a scorpion can tell the distance of the beetle from the difference \( \Delta t \) in the arrival times of the waves at its leg nearest the beetle. What is that time difference if the distance to the beetle is \( 37.5 \text{ cm} \)?