A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40kHz. During one fast swoop directly toward a flat wall surface. The bat is moving at 0.03 times the speed of sound in air. What frequency does the bat hear reflected off the wall ?

Explanation

Here, the frequency of sound emitted by the bat,`v=40kHz. `
Velocity of bat, `upsilon_(s)=0.03upsilon` , where upsilon is velocity of sound.
Apparent frequency of sound striking the wall
`v^(')=(upsilonxxv)/(upsilon-upsilon_(s))=(upsilon)/(upsilon-0.03upsilon)xx40kHz=(40)/(0.97)kHz`
This frequency is reflected by the wall and is received by the bat moving towards the wall. So `upsilon_(s)=0, upsilon_(L)=0.03upsilon.`
`v^('')=((upsilon+upsilon_(L))v^('))/(upsilon)=((upsilon+0.03upsilon))/(upsilon)((40)/(0.97))=(1.03)/(0.97)xx40kHz =42.47kHz`