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A detailed proof of the incorrectness of the classical wave equation is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The proof leads to the following irrefutable statement: The classical wave equation and the derivation of the classical wave equation are a gross error in mathematics and physics. The proof of this statement is based on the following irrefutable main results:
1.The first gross error is the following approximaterelationship: “sine of angle is approximately equal totangent of angle; cosine of angle is approximatelyequal to 1”. This relationship means (implies) that thequantity of the angle and the right-angled triangle donot exist. Consequently, the relationship between thetangent of the angle and the derivative of thedisplacement with respect to coordinate does notexist;
2.The second gross error is that the second-orderderivative of the displacement with respect tocoordinate does not exist, because the dimensions ofdisplacement and coordinate are “meter”, the first-order derivative of the displacement with respect tocoordinate is dimensionless quantity (i.e. the first-order derivative of the displacement respect tocoordinate has no the dimension “meter”);
3.The third gross error is that the first-order derivativeof the displacement with respect to coordinate cannot
be expanded into the Taylor series, because the second-order derivative of the displacement with respect to coordinate does not exist;
4.The fourth gross error is as follows:
a)The left side of the wave equation containsthe condition that time is a variable quantity,and the coordinate is a constant quantity;
b)The right side of the wave equation containsthe condition that time is a constant, and thecoordinate is a variable. This means (implies)that the equation contains contradictoryconditions (propositions). Therefore, theequation represents a violation of the formal-logical law of the lack (absence) ofcontradiction;
5.The fifth gross error is that the standard derivation ofthe equation relies on the following false theories:negative number theory, complex numbers theory,trigonometry, vector calculus, differential calculus, andNewton's second law.
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