Abat 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 5.59 104 hz, and if the speed of sound in air is 343 m/s, what is the smallest insect a bat can detect? answer in units of mm

6.136 mm

Explanation:

given,

frequency emitted by the bat = 5.59 x 10⁴ Hz

speed of sound = 343 m/s

smallest insect bat can hear  will be equal to the wavelength  of the sound the bat make.

λ = 6.136 mm

so, the smallest size of insect that bat can hear is equal to 6.136 mm

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .