Horseshoe bats (genus ) emit sounds from their nostrils and then listen to the frequency of the sound reflected from their prey to determine the prey's speed. (the "horseshoe" that gives the bat its name is a depression around the nostrils that acts like a focusing mirror, so that the bat emits sound in a narrow beam like a flashlight.) a flying at speed emits sound of frequency ; the sound it hears reflected from an insect flying toward it has a higher frequency . (a) show that the speed of the insect is where is the speed of sound. (b) if 80.7 khz, 83.5 khz, and 3.9 m/s, calculate the speed of the insect.