# The smallest insect a bat can detect are approximately the size of one wavelength of the sound the bat makes. a) what minimum frequency of the sound is necessary for the bat to detect an insect 0.57cm long? b) what is the period of the wave?

Jun 16, 2018

a. $f \cong 580 k H z$
b. $T = 1.7 \cdot {10}^{-} 6 s$

#### Explanation:

a. The formula that relates frequency and wavelength is

$f = \frac{v}{\lambda}$

where f is frequency, v is the velocity of propagation (velocity of sound in this case), and $\lambda$ is the wavelength.

To detect this fly, $\lambda$ needs to be $5.7 \cdot {10}^{-} 4 m$, (or shorter). Using $331 \frac{m}{s}$ for the speed of sound,

$f = \frac{331 \frac{\cancel{m}}{s}}{5.7 \cdot {10}^{-} 4 \cancel{m}} = 58.07 \cdot {10}^{4} {s}^{-} 1 \cong 580 k H z$

b. Period, $T$, is the reciprocal of frequency.

$T = \frac{1}{f} = \frac{1}{58.07 \cdot {10}^{4} {s}^{-} 1} = 0.0172 \cdot {10}^{-} 4 s \cong 1.7 \cdot {10}^{-} 6 s$

I hope this helps,
Steve