Horseshoe bars (genus Rhinolophus) 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 €œhorseshoe" that gives the hat its name is a depression around the nostrils that acts like a
Focusing mirror, so that the hat emits sound in a narrow beam like a flashlight.) A Rhinolophus flying at speed ubat emits sound of frequency fbat; the sound it hears reflected from an insect flying toward it bas a higher frequency fref.
(a) Show that the speed of the insect is

where u is the speed of sound.
(b) If fbat = 80.7 kHz. fref = 83.5 kHz, and ubat = 3.9 m/s, calculate the speed of the insect.

Transcribed Image Text:

Vai) - foat (v + Voat) - „frea (v - vsu) – foa (v + Vra) Vinsect fren (v - Ubat) + foat (v+ Vout) Linn (v