# 拍频

${\displaystyle y_{\mathrm {1} }=R\sin(k_{\mathrm {1} }x-\omega _{\mathrm {1} }t)}$
${\displaystyle y_{\mathrm {2} }=R\sin(k_{\mathrm {2} }x-\omega _{\mathrm {2} }t)}$

${\displaystyle k_{\mathrm {1} }\doteqdot k_{\mathrm {2} }\doteqdot k}$
${\displaystyle \omega _{\mathrm {1} }\doteqdot \omega _{\mathrm {2} }\doteqdot \omega }$

${\displaystyle y=y_{\mathrm {1} }+y_{\mathrm {2} }}$
${\displaystyle y=2R\sin({\frac {k_{\mathrm {1} }+k_{\mathrm {2} }}{2}}x-{\frac {\omega _{\mathrm {1} }+\omega _{\mathrm {2} }}{2}}t)\cos({\frac {k_{\mathrm {1} }-k_{\mathrm {2} }}{2}}x-{\frac {\omega _{\mathrm {1} }-\omega _{\mathrm {2} }}{2}}t)}$

${\displaystyle k'={\frac {k_{\mathrm {1} }-k_{\mathrm {2} }}{2}}={\frac {\Delta k}{2}}}$
${\displaystyle \omega '={\frac {\omega _{\mathrm {1} }-\omega _{\mathrm {2} }}{2}}={\frac {\Delta \omega }{2}}}$

${\displaystyle y=2R\sin(kx-\omega t)\cos(k'x-\omega 't)}$

## 延伸閱讀

• Thaut, Michael H. Rhythm, music, and the brain : scientific foundations and clinical applications 1st in paperback. New York: Routledge. 2005. ISBN 978-0415973700.
• Berger, Jonathan; Turow, Gabe (编). Music, science, and the rhythmic brain : cultural and clinical implications. Routledge. 2011. ISBN 978-0415890595.