Precalc Sine Project: Bat & Dolphin Echolocation

[egan94]

1. Homework Statement
I am doing a project for my precalc class which explores the applications of sine waves in real life. I chose to do bat and dolphin echolocation. so far the information i have found online has given me frequency in Hz, length of each pulse, and intensity in db. I'm pretty sure that the frequency and periods are correct but I am almost positive that my amplitude is wrong. Please help! I have been working on this all day and the project is due tonight at 9!

the numbers for bats are:Bat frequency: 14,000-100,000Hz
Each pulse last .2-100 milliseconds
intensity= 60-110 db

dolphins:Click duration: 50 to 128 microsecond
Travels at 1.5 km/sec
Frequency: 2,000 to 150,000 Hz
Intensity: 150 dB
2. Homework Equations



3. The Attempt at a Solution

my calculations for bats:
Frequency: 14,000 Hz
period= 1/frequency= 2π/b
2π/b=1/14,000
b=28,000π
Amplitude: intensity=60 to 110db
110-60=50db
Vertical shift up 50 since intensity can’t be less than zero
Y=asin(bt+c)
Y=50sin(28,000π)+50

how do i solve the amplitude with the information i have gathered?

 

[nate808]

it is important to always double check your calculations and make sure that your assumptions are correct. In this case, it seems that you have correctly calculated the frequency and period for the bat echolocation, but your amplitude calculation may be incorrect.

To calculate the amplitude, you can use the equation A = √(2I/ρv), where A is the amplitude, I is the intensity, ρ is the density of the medium (in this case, air), and v is the speed of the wave.

Using the given information for the bat echolocation, we can plug in the values and solve for the amplitude:

A = √(2(110 dB)/(1.2 kg/m^3 * 340 m/s)) = 0.86 m

This means that the amplitude of the bat's echolocation wave is 0.86 meters.

For the dolphin echolocation, you can use the same equation but with the given information for the dolphin:

A = √(2(150 dB)/(1.03 kg/m^3 * 1500 m/s)) = 0.98 m

This means that the amplitude of the dolphin's echolocation wave is 0.98 meters.

Remember to always check your units and make sure they are consistent. In this case, the units for the density of air and the speed of sound are in the SI unit system, so make sure to convert the values accordingly if needed.

I hope this helps you with your project and good luck with your deadline!