Bats can detect small insects that are about equal in size to the wavelength of the sound the bat makes with its echolocation system. A bat emits chirps at a frequency of 17.7kHz. Using the speed of sound as 340m/s, what is the smallest insect the bat can detect?
wavelength=speedsound/freuency
wavelength = v/f v is the wave speed
f is the frequency
1 kHz = 1000 Hz
340/(17.7*1000)
= 0.0192m
To determine the smallest insect the bat can detect, we need to calculate the wavelength of the sound the bat makes and compare it to the size of the insect.
The formula to calculate wavelength (λ) is:
λ = v / f
where:
- λ is the wavelength
- v is the speed of sound
- f is the frequency of the sound wave
Given:
- Bat's frequency (f) = 17.7 kHz = 17,700 Hz
- Speed of sound (v) = 340 m/s
Let's calculate the wavelength:
λ = 340 m/s / 17,700 Hz
λ = 0.0192 meters
Now, we have the wavelength of the sound emitted by the bat, which is approximately 0.0192 meters.
For the bat to detect an insect, the size of the insect should be equal to or larger than the wavelength of the sound wave. In this case, the smallest insect the bat can detect is an insect approximately 0.0192 meters (19.2 mm) or larger in size.