physics question?

Question

i cant seem to understand this question; i tried it many times but still cant seem to get it.

a bat uses echolocation to find insects. waves can only be used to detect objects that are one wavelenghth long or greater. if the bats echolocation is to be able to detect an insect that is 0.450 cm long on a night when the temperature is 15 degreed celcius, what must be the frequency that it uses to locate the insect? (Hint: some bats use frequencies as high as 150 kHz)

how do i do this? please help!!

Answer 1

Divide the speed of sound, which I estimate will be around 340 meter/sec at that temp, by the wavelength, which is .45 cm.
Firtst, convert the meters to cm: 340*100 = 34000.
Then divide by .45 cm.
34000/.45 = 75555.55 Hz, or 75.555 KHz.

Answer 2

Wavelength is related to frequency by the speed of propagation of the wave. f=speed/wavelength. This is true for any wave, wether it be waves on water or light waves or sound waves in this case.
The speed of sound in air is ~344meters/second at sea level and at 25 degrees celcius. The density of air changes at different elevations and temperature and the speed of sound(the speed at which waves propagate through air) is dependant on the air's density. You'll have to go to a chart or find a formula somewhere to either calculate the density of air or the speed of sound under various conditions. Since your problem doesn't mention an elevation, you can assume sea level.