Hey guys, I'm reading the(adsbygoogle = window.adsbygoogle || []).push({}); Theory of Soundand I've come to a part in which I'm having trouble double-checking the algebra.

Suppose we have two harmonic sound waves of equal amplitude traveling directly perpendicular to each other.

\begin{align} u=acos(2πnt-ε) && v=bcos(2πnt) \end{align}

They may then combine ifis eliminated to form the general ellipse:t

\begin{equation} \frac{u^2}{a^2}+\frac{v^2}{b^2}-\frac{2uv}{ab}cos(ε)-\sin^2{ε}=0 \end{equation}

My initial approach was to change forms to:

\begin{align} \frac{u}{a}=cos(2πnt-ε) && \frac{v}{b}=cos(2πnt) \end{align}

and then expand the cosine term in theequation, trying to eventually mold its transcendental functions into forms of \begin{equation} cos(2πnt) \end{equation} so I may then substitute in as \begin{equation} \frac{v}{b} \end{equation}u

After a few hours of expansion and resubstitution, I keep arriving at redundant answers. I tried working backwards from the equation given by changing forms to

\begin{equation} \frac{u^2}{a^2}+\frac{v^2}{b^2}-\frac{2uv}{ab}cos(ε)-(1-\cos^2{ε})=0 \end{equation}

and then I tried factoring, but I don't think this is the right approach.

If anyone has experience with combining transcendental functions and their relations to conics, any advice would be appreciated! Thanks!

~HL

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Help eliminating parameter for harmonic trig combination

Loading...

Similar Threads - Help eliminating parameter | Date |
---|---|

B Super basic polynomial and exponent definition help | Feb 20, 2018 |

I Question about the Divisor Function/Sums and Project Euler | Feb 16, 2018 |

B Using trig to find distance? | Jan 18, 2018 |

I Help manipulating a Physics equation | Nov 15, 2017 |

How do you eliminate one term of several in a denominator? | Jan 8, 2016 |

**Physics Forums - The Fusion of Science and Community**