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 7.69  10⁴ Hz, and if the speed of sound in air is 343 m/s, what is the smallest insect a bat can detect?

 mm

 

λ = 4.46mm the size of insect the bat can detect

Step-by-step explanation

Given:

• bats chirp at a frequency f = 7.69 x 10⁴ Hz,
• the speed of sound in air v = 343 m/s
• Size of insect = λ = 1 wavelength = unknown

Solve for: smallest insect the bat can detect

Solution:

To get the smallest insect the bat can detect, we have to get the equivalent wavelength that a frequency f= 7.69 x 10⁴ Hz at a speed of v=343m/s can perceive. To solve for wavelength we can use the formula v_w = fλ where v_w is the speed of sound in air = 343m/s and f is the frequency 7.69x10⁴/s.

343m/s=7.69x10⁴/s x λ

λ = 0.00446m

λ = 4.46mm the size of insect the bat can detect