Question

On a 20∘C∘C night, a bat hovering in the air emits an ultrasonic chirp that has a frequency of 45 kHzkHz. It hears an echo 60 msms later.

Suppose the bat’s timing uncertainty is ±1 msms; that is, what the bat perceives as a 60 msms delay could actually be anywhere in the range 59–61 msms. What is the uncertainty in the distance to the object?

Answer 1

The uncertainty in the distance to the object is 0.343 meters.

Step-by-step explanation:

The uncertainty in the distance to the object can be determined by calculating the minimum and maximum distances based on the given timing uncertainty. In this case, the bat hears an echo 60 ms later with a timing uncertainty of ±1 ms. This means that the actual delay could be anywhere in the range of 59-61 ms.

To calculate the uncertainty in distance, we can use the formula:

uncertainty in distance = speed × uncertainty in time

The speed of sound in air is approximately 343 m/s. Plugging in the values, we get:

uncertainty in distance = 343 m/s × 0.001 s = 0.343 m

Therefore, the uncertainty in the distance to the object is 0.343 meters.