# The Hearing of a bat

1. Jan 5, 2010

### sphouxay

1. The problem statement, all variables and given/known data

Bats are mainly active at night. They have several senses that they use to find their way about, locate prey, avoid obstacles, and "see" in the dark. Besides the usual sense of vision, bats are able to emit high-frequency sound waves and hear the echo that bounces back when these sound waves hit an object. This sonar-like system is called echolocation. Typical frequencies emitted by bats are between 20 and 200 kHz. Note that the human ear is sensitive only to frequencies as high as 20 kHz
A moth of length 1.0 cm is flying about 1.0 m from a bat when the bat emits a sound wave at 80.0 khz . The temperature of air is about 10.0 celsius. To sense the presence of the moth using echolocation, the bat must emit a sound with a wavelength equal to or less than the length of the insect.

The speed of sound that propagates in an ideal gas is given by

velocity = squareroot of(( (gamma = 1.4)*RT)/M

where gamma is the ratio of heat capacities (gamma = 1.4 for air), T is the absolute temperature in kelvins (which is equal to the Celsius temperature plus 273.15), M is the molar mass of the gas (for air, the average molar mass is 28.8 *10^-3 kg/mol), and R is the universal gas constant (R=8.314 j*mol^-1*K^-1).

Find the wavelength of the 80.0-khz wave emitted by the bat

Will the bat be able to locate the moth despite the darkness of the night?

2. Relevant equations

Wavelength = velocity/frequency

velocity = squareroot of(( (gamma = 1.4)*RT)/M

3. The attempt at a solution

Ill get back with my attempts as of now im very flustered.

2. Jan 5, 2010

### mgb_phys

Step 1, just find the speed of sound in air (hint look up the approx answer to check)
Step 2, find the frequency (check your units)

3. Jan 5, 2010

### sphouxay

the speed of sound in air at 20 degree celsiusis is 343 m/s, my calculation with the ideal gas law is 338.28 is that correct? And for the frequency wouldnt I just have to divide the velocity of 338.28 by 80 khz. Is that even close 4.2285

4. Jan 5, 2010

### mgb_phys

Yes - except you want it at 10c.
The speed of sound is one of those numbers you shoudl have a rough idea of just so you can check your answer.

Be careful with the units in your answer, make sure everythign is in m and s-1

5. Jan 6, 2010

### sphouxay

I did use 10 degree celsius which would be 273 + 10 (Conversion from celsius to kelvins) and I recieved 338.28. If my final answer is 4.2285 what am I converting that to to get my m and s^-1