# Electromagnetic Waves - Class 12 - Physics

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## Extra Questions - Electromagnetic Waves | NCERT | Physics | Class 12

The displacement ($x$) of a particle as a function of time ($t$) is given by:

$$ X = a \sin (bt + c) $$

Where $a$, $b$, and $c$ are constants of motion. Choose the correct statement(s) from the following:

A. The motion repeats itself in a time interval $\frac{2 \pi}{b}$.

B. The energy of the particle remains constant.

C. The velocity of the particle is zero at $x = \pm \alpha$.

D. The acceleration of the particle is zero at $x = \pm \alpha$.

The correct answer is **Option A: The motion repeats itself in a time interval $\frac{2\pi}{b}$.**

**Reasoning:**

The displacement of the particle as given by the equation $X = a \sin(bt + c)$ implies that the particle is undergoing

**simple harmonic motion**. In simple harmonic motion, the displacement function is cyclic and repeats after a period.To determine when the motion repeats itself, observe how the function behaves over time: $$ X(t) = a \sin(bt + c) $$ and when $t$ is increased by $\frac{2\pi}{b}$, $$ X\left(t + \frac{2\pi}{b}\right) = a \sin\left( b(t + \frac{2\pi}{b}) + c \right) = a \sin(bt + c + 2\pi) $$ Since $\sin(\theta + 2\pi) = \sin(\theta)$, we get: $$ X\left(t + \frac{2\pi}{b}\right) = a \sin(bt + c) = X(t) $$ Thus, the displacement $X$ at time $t + \frac{2\pi}{b}$ is the same as at time $t$, confirming that the motion indeed repeats every $\frac{2\pi}{b}$ seconds.

**Option B**: This statement, although not part of the typical descriptions given here, can be analyzed intuitively in simple harmonic motion where kinetic and potential energies transform into each other but the total mechanical energy remains constant.**Option C and D**: Although velocity becomes zero at the extreme points of the simple harmonic motion (i.e., $x = \pm \alpha$ where $\alpha$ is amplitude $a$), the statements regarding acceleration are incorrect. Acceleration is in fact maximum at the extremes of the motion, directly proportional to the displacement from the mean position (i.e., $x = \pm a$) due to the restoring force being maximum at these points.

To summarize: **Option A** is most specifically and confidently correct based on the provided expression and principles of simple harmonic motion. Other options (C and D) contain inaccuracies, and B lacks specific context in the given solution.

A longitudinal wave is propagating along the $x$-axis. Particles of the medium vibrate along

A $x$-axis

B $y$-axis

C $z$-axis

D None of these

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In Australia, people are suffering from skin cancer due to $\qquad$ from the sun.

A) gamma rays

B) ultraviolet rays

C) infrared rays

D) visible rays