Question

What does the $y$ coordinate in the general wave equation $f(x - vt)$ represent?
A. Displacement of wave along $y$ axis
B. Displacement of particle along $y$ axis
C. Displacement of energy along $y$ axis
D. Displacement of momentum along $y$ axis

Answer 1

The given general wave equation represents a forward propagating wave where the x-coordinate gives us the direction of the wave and the second part gives us the distance travelled by the wave and we need to find what the y-coordinate represents.

Complete answer:
When particles oscillate about their mean positions at different phases produces a wave motion. Wave motion is a periodic motion that replicates itself after an equal interval of time. Wave motion is a method of transfer of energy. There are two types of waves namely longitudinal and transverse waves.

Longitudinal waves have oscillations parallel to the direction of propagation of the wave whereas transverse waves have oscillations perpendicular to the direction of the propagation of the wave.Now in the given wave equation $f(x - vt)$, $f$ represents the frequency of the oscillations, $x$ represents the direction of propagation of the wave, $v$ represents the velocity and $t$ represents time. Therefore the $y$ coordinate represents the displacement of the wave.

Hence, the correct answer is option A.

Additional information: Now waves can be divided into two categories depending on the transfer of energy. A stationary wave is formed by the superposition of two equal progressive waves and is confined to a particular space whereas a progressive wave is formed due to continuous vibration of the particles of the medium. Energy is not transferred in standing waves whereas in progressive waves energy is transferred from point to point as the wave propagates forward.

Note: The given equation calculates the displacement of the wave for a particular direction at a given time. If the wave propagates in the opposite direction, the negative sign in the equation would change to positive as the direction of the wave would be in the negative x-direction.