A bat can detect small objects, such as an insect, whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a frequency of 8.31 104 Hz, and if the speed of sound in air is 343 m/s, what is the smallest insect a bat can detect?

_______________ mm

L = V * (1/F).

L = 343m/s * (1/8.31*10^4)s=41.28*10^-4m
= 4.13 mm.

To determine the smallest insect a bat can detect, we need to find the wavelength of the sound wave emitted by the bat. We can then compare this wavelength to the size of the insect.

The relationship between frequency (f), wavelength (λ), and the speed of sound (v) is given by the formula:

v = f * λ

Rearranging the formula, we can solve for wavelength:

λ = v / f

Given:
Frequency, f = 8.31 x 10^4 Hz
Speed of sound in air, v = 343 m/s

Substituting the given values into the formula, we can calculate the wavelength of the sound wave:

λ = 343 m/s / 8.31 x 10^4 Hz

Calculating the result:

λ ≈ 0.00413 meters

To convert from meters to millimeters, we multiply by 1000:

λ ≈ 4.13 mm

Therefore, the smallest insect a bat can detect is approximately 4.13 mm in size.