Particle velocity in transverse and longitudinal waves

Steps:

• Recall that in progressive waves, particle displacement varies sinusoidally with time and position.
• For both transverse and longitudinal waves, particle velocity is the derivative of displacement, given by $v = -\omega A \sin(\omega t - kx + \phi)$.
• Maximum velocity occurs when displacement is zero, as $\sin$ reaches 1 when the sine argument is $\pi/2$, where displacement cosine is zero.
• This holds for both wave types since the velocity-displacement relation is identical.

Why C is correct:

• In simple harmonic motion underlying both waves, velocity $v = \pm \omega \sqrt{A^2 - y^2}$, so at zero displacement , speed is maximum .

Why the others are wrong:

• A: Electromagnetic transverse waves propagate without a medium.
• B: Wave speed depends on medium properties, so transverse and longitudinal speeds differ (e.g., sound vs. light in air).
• D: Longitudinal waves involve particle oscillation parallel to propagation direction, unlike transverse.

Final answer: C