Question

Statement-1: The superposition principle is applicable only for small disturbances.
Statement-2: The superposition principle is applicable only for nonlinear waves.
A) If both the statements are true and statement 2 is the correct explanation of statement 1.
B) If both the statements are true and statement 2 is not the correct explanation of statement 1.
C) If statement 1 is true and statement 2 is false.
D) If statement 1 is false and statement 2 is true.

Answer 1

Hint: The superposition principle states that, for all linear systems, when two or more waves overlap one another, the net response is the algebraic sum of the individual waves. This principle is violated in the case of large disturbances.

Complete step-by-step solution:
The superposition principle states that when two or more waves overlap one another, the resultant disturbance is equal to the algebraic sum of the individual disturbances (individual waves). The superposition principle is applied, whenever two or more waves are traveling through the same medium at the same time. The waves pass through each other without being disturbed. The net displacement of the medium at any time or point of space is the sum of the individual wave displacements. Normally, linear waves obey the principle of superposition - which means that the amplitudes of two waves traveling through the same medium at the same time are added together. Linear waves interfere with each other by adding their amplitudes together. But, nonlinear waves do not obey the principle of superposition, and instead of interacting through interference and simple addition, they collide in a complicated and nonlinear manner. The resultant wave is not the sum of the two individual waves. This implies that the superposition principle does not apply to the nonlinear waves.
The superposition principle is valid only for waves with small amplitude or for small disturbances. Because the algebraic sum of the waveforms is produced by waves acting separately. Since small amplitude waves move independently, it is applicable for small disturbances.

Therefore, statement 1 is true, but statement 2 is wrong. The answer is option C.

Note: Linear waves are described by the linear equations. In the linear equation, the dependent variable and its derivatives are raised to the first power. Nonlinear waves are described by the nonlinear equations and they have a shape that is not a straight line.