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?

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.

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