Define longitudinal and transverse waves. Find the displacement equation of a plane progressive wave. Also define the following terms: (a) Amplitude (b) Frequency (c) Wavelength (d) Phase

**OR**

Write down the principle of superposition of waves. Using this principle, obtain th

Question

Define longitudinal and transverse waves. Find the displacement equation of a plane progressive wave. Also define the following terms: (a) Amplitude (b) Frequency (c) Wavelength (d) Phase

**OR**

Write down the principle of superposition of waves. Using this principle, obtain the expression for the resultant amplitude due to the superposition of two waves.

Accepted Answer

>

> [!TLDR]
> Longitudinal waves vibrate parallel to propagation, transverse waves vibrate perpendicular to it; a plane progressive wave is described by $y = A\sin(\omega t - kx)$, with amplitude, frequency, wavelength and phase as its key descriptive terms.
>
> (This question offered an OR alternative on the principle of superposition; answering the primary part on wave types and the progressive wave equation.)
>
> **Longitudinal waves:** waves in which the particles of the medium vibrate back and forth along the same direction as the wave travels (parallel to propagation), producing alternating regions of compression (particles closer together) and rarefaction (particles farther apart). Sound waves in air are the standard example.
>
> **Transverse waves:** waves in which the particles of the medium vibrate perpendicular to the direction the wave travels, producing alternating crests (highest points) and troughs (lowest points). Waves on a stretched string, and electromagnetic waves, are examples (transverse waves require a medium with shear elasticity, so they cannot travel through fluids/gases in the mechanical case, unlike longitudinal waves).
>
> **Displacement equation of a plane progressive wave:** for a sinusoidal wave travelling in the $+x$ direction, the displacement $y$ of a particle at position $x$ and time $t$ is
>
> $$y(x,t) = A\sin(\omega t - kx)$$
>
> where $\omega = 2\pi f$ is the angular frequency and $k = 2\pi/\lambda$ is the wave number (propagation constant). This equation is obtained by recognising that a particle at position $x$ repeats, with a time delay $x/v$, the same motion as the particle at the origin, giving $y(x,t) = A\sin\!\big(\omega(t - x/v)\big) = A\sin(\omega t - kx)$ since $k = \omega/v$.
>
> **Defining the key terms:**
> - **(a) Amplitude ($A$):** the maximum displacement of a particle of the medium from its mean (equilibrium) position during one oscillation.
> - **(b) Frequency ($f$):** the number of complete oscillations mad

Q.Define longitudinal and transverse waves. Find the displacement equation of a plane progressive wave. Also define the following terms:

Concept understanding — Wave Type Classification

Wave Type Classification: From Intuition to Precision

The Core Intuition

The Precise Classification

Transverse Waves

Longitudinal Waves

Why This Matters

Q.Define longitudinal and transverse waves. Find the displacement equation of a plane progressive wave. Also define the following terms:

🎓Unlock everything free for 14 days

Unlock everything free for 14 days