Question

Bats can detect small objects, such as insects, that are approximately the size of one wavelength. If a bat emits a chirp at a frequency of 60.0 kHz and the speed of sound waves in air is 330 m/s, what is the size of the smallest insect that the bat can detect? Answer in mm.

Answer 1

Given:

Frequency, f = 60.0 kHz

Speed of sound waves, v = 330 m/s

Let's find the smallest insect that the bat can detect.

To find the smallest insect the bat can detect, apply the wavelength formula:

`\lambda=(v)/(f)`

Where:

• λ is the wavelength (size of the smallest insect the bat can detect).

,

• v is the speed of sound waves in air = 330 m/s

,

• f is the frequency in Hz = 60.0 kHz = 60.0 x 10³ Hz.

Thus, we have:

`\begin{gathered} \lambda=(330)/(60*10^3) \\ \\ \lambda=(330)/(60000) \\ \\ \lambda=0.0055\text{ m} \end{gathered}`

Now convert from meters(m) to millimeters (mm).

Where:

1 m = 1000 mm

Hence, we have:

`0.0055m*1000=5.5\text{ mm}`

Therefore, the size of the smallest insect the bat can detect is 5.5 mm.

ANSWER:

5.5 mm