Question

Since sound is generated by vibrations and travels in waves it can be modeled by trigonometric functions. When an object vibrates twice as fast, it produces a sound with a pitch one octave higher than before. Amplitude is associated with loudness. Suppose a sound can be modeled with the function g(è)= 15sin(200è)

a) Write a function for a sound with the same pitch as the sound modeled by g but 3 times as loud.

b) Write a function for sound with the same volume as the sound modeled by g but one octave higher.

c) Write a function for a sound with the same volume as the sound modeled by g but 2 octaves higher


Thanks for the help (this is due by May 13, 2011)

Answer 1

I will make it easy for you, nice me.

g(t)= Amplitude*sin (2PI*frequency*time)

That is the base form. In your case, amplitude is initially 15 and frequency is 200/2PI

Answer 2

What do you mean by
^three times as loud" ? If loudness is a measure of power per area, then the amplitude has to be higher by the square root of three.

To the ear, this will correspond to about 4.8 decibels more of sound level, not "three times as much".