Mathematics but no physics——Morse theory of forced vibration in a room

Classical normal-mode theory gives only the reverberant sound field in a room without the direct sound. Apparently it is wrong. But the theory was ever supported because it complied exactly with the traditional treatment of a distributed system of vibration. The question persisted for more than half a century. It is suggested that the mistaken result is not the matter of mathematical treatment, but that of physical insight, the treatment's wrong start about sound source assumption. A theory of double sound source is proposed. Realized it in the equation of wave motion, after solving, the correct result of sound field in a room is obtained, conforming both with experiments and common knowledge. Under certain conditions, the result is approximated to a form, essentially agrees with the formula obtained from energy considerations of sound field in room. This problem shows definitely that the physics analysis is indispensable, in the scientific research work, although mathematical treatment and experiments are important.