Bats chirp at high frequencies that humans cannot hear. They use the echoes to detect small objects, such as insects, as small as one wavelength. If a bat emits a chirp at a frequency of 60.0 kHz and the speed of sound waves in air is 340 m/s, what is the size in millimeters of the smallest insect that the bat can detect?

Question

Biology

Gary Davila

3 July, 12:16

Bats chirp at high frequencies that humans cannot hear. They use the echoes to detect small objects, such as insects, as small as one wavelength. If a bat emits a chirp at a frequency of 60.0 kHz and the speed of sound waves in air is 340 m/s, what is the size in millimeters of the smallest insect that the bat can detect?

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Answers (1)

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Kelvin Mosley · Answer 1

The answer is 5.7 mm.

To calculate this we will use the formula that represents correlation between a frequency (f), a speed of sound waves (v), and the wavelength (λ):

v = λ * f ⇒ λ = v : f

It is given:

v = 340 m/s

f = 60 kHz = 60,000 Hz = 6000 1/s (Since f = 1/T, the unit is Hz = 1/s)

λ = ?

Thus:

λ = 340 m/s : 60,000 1/s = 0.0057 m = 5.7 mm

It is said bats use the echoes to detect insects as small as one wavelength. Since the wavelength is 5.7 mm, that means that bats can detect insects 5.7 mm small.