On a 20ºC night, a bat hovering in the air emits an ultrasonic chirp that has a frequency of 45 kHz. It hears an echo 54 ms later. a. Suppose the bat's timing uncertainty is +1 ms; that is, what the bat perceives as a 54 ms delay could actually be anywhere in the range 53-55 ms. What is the uncertainty in the distance to the object? b. Suppose the object is an insect flying straight away from the bat. What is the insect's speed if the ultrasonic echo is shifted down in frequency by 750 Hz?
On a 20ºC night, a bat hovering in the air emits an ultrasonic chirp that has a frequency of 45 kHz. It hears an echo 54 ms later. a. Suppose the bat's timing uncertainty is +1 ms; that is, what the bat perceives as a 54 ms delay could actually be anywhere in the range 53-55 ms. What is the uncertainty in the distance to the object? b. Suppose the object is an insect flying straight away from the bat. What is the insect's speed if the ultrasonic echo is shifted down in frequency by 750 Hz?
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VIEWStep 2: Calculate the maximum and minimum value of the distance between the observer and the source:
VIEWStep 3: Find the expression for the uncertainty in the distance:
VIEWStep 4: Calculate the uncertainty in the distance:
VIEWStep 5: Find the expression for the speed of the bug:
VIEWStep 6: Calculate the speed of the bug:
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