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 50.0 kHz, and if the speed of sound in air is 340 m/s, what is the smallest insect a bat can detect?
calculate the wavelength.
frequency*wavelength=speedsound
To determine the smallest insect a bat can detect, we need to calculate the wavelength of the sound wave first.
The speed of sound in air is given as 340 m/s, and we know that the frequency of the bat's chirp is 50.0 kHz (50,000 Hz).
The formula to calculate the wavelength (λ) of a sound wave is:
λ = v/f
Where:
λ = Wavelength
v = Speed of sound
f = Frequency
Plugging in the given values into the formula, we have:
λ = 340 m/s / 50,000 Hz
λ ≈ 0.0068 meters (6.8 millimeters)
Therefore, the smallest insect that a bat can detect is approximately equal to the wavelength of its sound, which is about 6.8 millimeters.