second-order linear hyperbolic equation [Yoshikazu Kobayashi] Wave Equation in PhysicsIn general, in waves, a physical quantity u, such as the displacement of a medium or the components of an electric field or magnetic field, satisfies a second-order partial differential equation called the wave equation. A function u that satisfies the wave equation is called a wave function. For a wave traveling in the x direction, the second partial differential coefficient ∂ 2 u/∂t 2 of the wave function u(x,t) with respect to time t is proportional to the second partial differential coefficient ∂ 2 u/∂x 2 with respect to the position coordinate x. In other words, ∂ 2 u/∂t 2 =v 2 (∂ 2 u/∂x 2 ), which is the (one-dimensional) wave equation. The v in the proportionality coefficient v 2 is the speed at which the wave travels. The general solution to this partial differential equation is [Yoshiro Kainuma] Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend |
二階線形双曲型方程式 [小林良和] 物理学における波動方程式一般に波においては、媒質の変位や、電場、磁場の成分のような物理量uが波動方程式とよばれる二階の偏微分方程式を満足する。波動方程式を満足する関数uは波動関数とよばれる。 x方向に進行する波については、波動関数u(x,t)の時間tに関する二階の偏微分係数∂2u/∂t2が、位置座標xに関する二階の偏微分係数∂2u/∂x2に比例する。すなわち∂2u/∂t2=v2(∂2u/∂x2)で、これが(一次元の)波動方程式である。比例係数v2のvは波の伝わる速度である。この偏微分方程式の一般解は、 [飼沼芳郎] 出典 小学館 日本大百科全書(ニッポニカ)日本大百科全書(ニッポニカ)について 情報 | 凡例 |
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