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The wave equation is a linear second-order partial differential equation which describes the propagation of oscillations at a fixed speed in some quantity y: ... Especially important are the solutions to the Fourier transform of the wave equation, which define Fourier series, spherical harmonics, and their generalizations.
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ᴛʜᴇ ᴡᴀᴠᴇ ᴇϙᴜᴀᴛɪᴏɴ ɪs ᴀ ʟɪɴᴇᴀʀ sᴇᴄᴏɴᴅ-ᴏʀᴅᴇʀ ᴘᴀʀᴛɪᴀʟ ᴅɪғғᴇʀᴇɴᴛɪᴀʟ ᴇϙᴜᴀᴛɪᴏɴ ᴡʜɪᴄʜ ᴅᴇsᴄʀɪʙᴇs ᴛʜᴇ ᴘʀᴏᴘᴀɢᴀᴛɪᴏɴ ᴏғ ᴏsᴄɪʟʟᴀᴛɪᴏɴs ᴀᴛ ᴀ ғɪxᴇᴅ sᴘᴇᴇᴅ ɪɴ sᴏᴍᴇ ϙᴜᴀɴᴛɪᴛʏ ʏ: ᴀ sᴏʟᴜᴛɪᴏɴ ᴛᴏ ᴛʜᴇ ᴡᴀᴠᴇ ᴇϙᴜᴀᴛɪᴏɴ ɪɴ ᴛᴡᴏ ᴅɪᴍᴇɴsɪᴏɴs ᴘʀᴏᴘᴀɢᴀᴛɪɴɢ ᴏᴠᴇʀ ᴀ ғɪxᴇᴅ ʀᴇɢɪᴏɴ
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