Bat sonar with temperature gradient at 40m distance

[Vanity]

Hi,

I'm having troubles finding a solution for a problem. Can anybody help me out ? I have no idea where to start so any informations is greatly appreciated. Here's the problem:

A bat uses sonar at 50kHz to detect objects. The bat is flying in air at 30 degrees celsius. Directly in front of the bat is a very rapid change of air temperature at 40m distance where the temperature drops to 8 degrees celsius. If the echo return is 1.34s, determine the distance to the bug.

Thanks a lot,
- alex

 

[member 553083]

To solve this problem, you will need to use the speed of sound in air. The speed of sound changes with temperature, so you'll need to calculate the average speed between the two temperatures (30 and 8 degrees celsius). The average speed is calculated by taking the weighted average of the two speeds based on the proportion of the distance travelled at each temperature. Once you have the average speed, you can calculate the distance travelled by the sound wave by dividing the time taken for the echo to return (1.34s) by the speed of sound: Distance = 1.34s / Average Speed. You can then add this distance to the 40m distance already given in the problem to get the total distance from the bat to the bug.