Two waves are represented by the equations y1=A sin(10 πx-15 πt+(π)/(2)) and y2=2 A sin(30 πx +4

step 1 In this question we have given two waves equation and we have to find that which of the followin

Two waves are represented by the equations y1=A sin(10 πx-15...

Two waves are represented by the equations $y_{1}=A \sin \left(10 \pi x-15 \pi t+\frac{\pi}{2}\right)$ and $y_{2}=2 A \sin (30 \pi x$ $+45 \pi t$ ). Which of the following statements is correct? (A) The maximum particle velocity of the second wave is twice that of first. (B) Their superposition will produce a standing wave. (C) Maximum particle acceleration for the second wave is eighteen times that of the first wave. (D) Their wave velocities are different.

Two waves are represented by the equations $y_{1}=A \sin \left(10 \pi x-15 \pi t+\frac{\pi}{2}\right)$ and $y_{2}=2 A \sin (30 \pi x$
$+45 \pi t$ ). Which of the following statements is correct?
(A) The maximum particle velocity of the second wave is twice that of first.
(B) Their superposition will produce a standing wave.
(C) Maximum particle acceleration for the second wave is eighteen times that of the first wave.
(D) Their wave velocities are different.

Key Concepts

Superposition Principle and Standing Waves

The superposition principle states that when two or more waves coexist in the same medium, the resultant displacement at any point is the algebraic sum of the displacements due to each individual wave. This principle explains interference effects, such as standing waves, which occur when waves of the same frequency and amplitude travel in opposite directions, leading to nodes and antinodes in the medium.

Wave Propagation Speed

Wave propagation speed is the rate at which a wave travels through a medium and is given by the ratio of the angular frequency to the wave number. This concept underlines the independence of the wave's speed from its amplitude in a non-dispersive medium and is key when analyzing the movement and interaction of different waves.

Wave Parameters

This concept refers to the characteristics of a sinusoidal wave, which are typically represented by its amplitude, angular frequency, wave number, and phase constant. These parameters define the shape, period, and spatial variation of the wave and are fundamental in describing any wave behavior mathematically.

Particle Velocity and Acceleration in Harmonic Motion

In harmonic motion, such as that described by a sinusoidal wave, the maximum particle velocity is obtained by multiplying the amplitude by the angular frequency, while the maximum acceleration is given by the product of the amplitude and the square of the angular frequency. This relationship is important when comparing the dynamic behavior of different waves.

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