Question

A startled moth is trying to evade a hungry bat hot on its trail, 3.00m behind it. (a) What would be the time delay in the bat emitting an ultrasonic pulse and receiving the echo for air temperatures of 5.00 C and 35.00 C? (b) Use this range to express the percent uncertainty in locating the moth.

Thank you in advance!

Answer 1

PART (A)

Velocity of sound in air is

where = 7/5 for diatomic gas

M = average molecular mass of air = 28.97 g/mol

T in kelwin

   V1 =velocity at 5.00C =331.18 m/s

V2 velocity at 35.00 C = 351.77 m/s

d = distance between bat and moth = 3 m

t1 = time to hear echo at 5.00 c = 2d/V1 = 0.018 sec

t2 = time to hear echo at 35.00 c = 2d/V2 = 0.017 sec

therefore time delay = t= t1 - t2 = 0.001 sec

Part (B)

% uncertainitity = 2 t/(t1+ t2) = 5.7%