What is the acoustic power of each pulse?

[rpullo]

Homework Statement

In search for insects, a bat uses an echolocating system based on pulses of high frequency sound. These pulses are 2.0 ms in duration, have a frequency of 50 kHz, and have an intensity level of 100 dB at 1.0 m from the bat's mouth. Assume that the bat produces spherical acoustic waves.

a.What is the acoustic power of each pulse?
b. A bug is located 5.0 m from the bat. The effective cross-sectionl area of the insect is 10 mm². How much of the acoustic power emitted by the bat is intercepted by the insect?

Homework Equations

I = P/A
E = Pt

The Attempt at a Solution

a. Given intensity level, I can find intensity...

10log(I/I₀) = 100 [I₀ = 10^-12
I = 0.01

P = 0.01 x 4 x [pi] x 1² = 0.13 W

Textbook has 0.12, so I was wondering if I did it correctly.

b. I found the intensity of the pulse at 5 m to be 3.8 x 10^-4 so...

P = AI = (0.001)(3.8 x 10^-4) = 3.8 x 10^-6

Textbook has it to power -10, so I'm wondering if someone can find a mistake..
Thanks!

 

[anathema]

Your calculations for part a seem correct. The slight difference in the answer could be due to rounding errors or different values for the constants used.

For part b, you have correctly found the intensity at 5 m. However, the power intercepted by the insect would be given by:

P = AI = (0.00001)(3.8 x 10^-4) = 3.8 x 10^-8 W

This is because the effective cross-sectional area of the insect is given in square millimeters, so it needs to be converted to square meters (hence the extra 0.00001 factor). The power intercepted is much smaller than the power of the pulse emitted by the bat, which makes sense since the insect is much smaller than the bat and is located further away.

I hope this helps clarify your doubts. Let me know if you have any further questions. Keep up the good work in your studies as a scientist!