: precalc project amplitude help

[egan94]

URGENT: precalc project amplitude help!

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

Homework Equations

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?

 

[Delphi51]

I don't have the answer, but perhaps can shed some light on the problem.
The 110 db you have is not an intensity (which would have units of watts per square meter) but rather a logarithmic scale of how much more intense this sound is compared to some standard intensity. Check this link: http://en.wikipedia.org/wiki/Sound_intensity#Sound_intensity_level
you could use its standard intensity to convert your db value into an intensity. Check the links at the bottom of the article - this one gives all kinds of conversion formulas (but none for amplitude):
http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf

Amplitude is more problematical. Amplitude of what? It could be the pressure of the sound wave. Or maybe the displacement of the medium as the wave passes through:

The amplitude of sound waves and audio signals (which relates to the volume) conventionally refers to the amplitude of the air pressure in the wave, but sometimes the amplitude of the displacement (movements of the air or the diaphragm of a speaker) is described. The logarithm of the amplitude squared is usually quoted in dB, so a null amplitude corresponds to −∞ dB. Loudness is related to amplitude and intensity and is one of most salient qualities of a sound, although in general sounds can be recognized independently of amplitude. The square of the amplitude is proportional to the intensity of the wave.
http://en.wikipedia.org/wiki/Amplitude

In short, amplitude probably isn't a useful quantity in your study.