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A bat flies at 8
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A bat flies at 8.00 m/s towards an insect that is moving away from it at a lower speed (i.e. the distance between the two is decreasing). The bat is emitting a steady sound of frequency 1600 Hz. It hears both the sound it emits, plus the sound reflected by the insect.
a) If the bat hears the sound 0.0400 s later, how far away is the bug? (2)
b) If the sound is emitted with a power of 100 W, what is the area of the insect if the bat hears the echo from the insect with an intensity level of 30 dB? (4)
c) How fast is the insect moving if the bat hears a beat frequency of 12 Hz? (4)
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(a) S = vt / 2
= 343 * 0.04 / 2
= 6.86 m
(b) I1 = Po / 4πr2
= 100 / 4 * 3.14 * (6.86)2
= 0.1692 W/m2
P1 = I1A
I2 = P1 / 4πr2
= I1A / 4πr2
= 0.1692 * A / 4 * 3.14 * (6.86)2
= (2.8624 * 10-4 * A) m2
30dB = 10 log10 I2 / Io
I2 = 10-12 * 103
= 10-9 = (2.8624 * 10-4 * A) m2
A = 3.494 * 10-6 m2
(c) f1 = (343 - x / 343 - 8) fo
f2 = (343 + 8 / 343 + x) f1
f2 = (343 - x / 343 + x) * (351 / 335) fo
343 - x / 343 + x = f2 / fo (335 / 351)
343 - x / 343 + x = (1612 / 1600) * (335 / 331) = 0.961574
343 - x = 329.82 + 0.961574x
x = 13.18 / 1.961574
x = 6.72 m/s
