Question

Would the diffraction of the waves (spreading out around obstacles like trees) be more or less of a problem if the bat used audible sound for detection (rather than ultrasound)?

Answer 1

Ultra sound has frequency of 20,000 Hertz and beyond

So = 330m/s/ 20000H = 0.017 mrs = 1.7cm

So ultra sound has wavelength 1.7 cm and below.

Now, diffraction is pronounced when obstacle has size similar to wavelength.

So trees which have width larger than 1.7 cm will not have pronounced diffraction effect and hence better echo formation,thus helping bats.

If bats use audible sound with mean frequency of 10000H

the wavelength would be 3.3cm

Now the effect of difraction is pronounced when the width of obstruction is of similar order as the sound waves.. So if sound of 10,000 Hz is used the diffraction would be pronounced when tree width is 3.3cm .

So with ultra sound bending woud be less pronounced in normal sized obstacles(like trees)and hence bats would be able to echo the sound from trees better.