# Wave Problem -- Total amplitude of fundamental and first three harmonics

• PhysicsMan999
In summary, an acoustic signal with a fundamental frequency of 463 Hz composed of the first three harmonics has a total amplitude of 0.626 at time 0.401 seconds, given the amplitude of the harmonics are 0.100, 0.300, and 0.760 and the phase angles are all set to 0. However, computing the trigonometric functions with such large angles may require more precision for accurate results.

## Homework Statement

1. An acoustic signal is composed of the first three harmonics of a wave of fundamental frequency 463 Hz. If these harmonics are described, in order, by cosine waves with amplitudes of 0.100, 0.300, and 0.760, what is the total amplitude of the signal at time 0.401 seconds? Assume the waves have phase angles θn = 0.

## Homework Equations

F(t)= Sum of Ancos(2nf1t-0n)

## The Attempt at a Solution

I simply plugged in the above values into the equation and got 0.00600897, -0.29783, and -0.136345. No idea where to go from here. Any assistance is appreciated!

PhysicsMan999 said:

## Homework Equations

F(t)= Sum of Ancos(2nf1t-0n)

## The Attempt at a Solution

I simply plugged in the above values into the equation and got 0.00600897, -0.29783, and -0.136345. No idea where to go from here. Any assistance is appreciated!
Not sure how you're getting those numbers. please post full working.

(0.1)*cos(2pi*463*0.401)=0.00600897
(0.300)+cos(4pi*463*0.401)= -0.29783
(0.760)*cos(6pi*463*0.401)= -0.136345

PhysicsMan999 said:
(0.1)*cos(2pi*463*0.401)=0.00600897
(0.300)+cos(4pi*463*0.401)= -0.29783
(0.760)*cos(6pi*463*0.401)= -0.136345
Hmmm...
I plugged (0.1)*cos(2*pi()*463*0.401) into OpenOffice Calc and it gives -0.052.
The trouble with computing trig functions of such large angles is that a lot of precision is needed.
I also tried (0.1)*cos(mod(2*pi()*463*0.401;2*pi())) and got the same result.
(In Excel you need to change the semicolon to a comma.)
What are you using for the calculation?
For the other two harmonics I get -0.14 and +0.76.

PhysicsMan999 said:
(0.1)*cos(2pi*463*0.401)=0.00600897
(0.300)+cos(4pi*463*0.401)= -0.29783
(0.760)*cos(6pi*463*0.401)= -0.136345
Ther argument of the cosine function is in radians, not degrees.
Then your numbers will agree with haruspex's.