This MCQ module is based on: Transverse Longitudinal Waves
TOPIC 29 OF 33
Transverse Longitudinal Waves
🎓 Class 11
Physics
CBSE
Theory
Ch 14 – Waves
⏱ ~14 min
🌐 Language: [gtranslate]
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Transverse Longitudinal Waves
14.1 Introduction
A ripple spreading on a pond, the sound from a sitar, light from a distant star, an earthquake shaking the ground — all are examples of waves. Although they look very different, they share remarkable common mathematical structure. A wave transports energy from one place to another without bulk transport of matter.
If you drop a stone in a still lake, ripples spread outward. Each leaf floating on the lake bobs up and down as the wave passes, but does NOT travel along with the wave. Only the disturbance propagates outward — the water itself stays largely in place. This is the essence of wave motion: it is a way of moving energy without moving the medium en masse.
14.2 Transverse and Longitudinal Waves
14.2.1 Transverse Waves
In a transverse wave, particles of the medium oscillate perpendicular to the direction in which the wave travels. Pluck a stretched string — pull a section sideways and release. A transverse pulse races along the string, while the string itself moves only up and down.
14.2.2 Longitudinal Waves
In a longitudinal wave, particles oscillate along the same direction the wave travels. Push and pull a Slinky lengthwise: alternating dense (compressions) and sparse (rarefactions) regions move outward.
| Property | Transverse | Longitudinal |
|---|---|---|
| Particle motion | Perpendicular to wave | Parallel to wave |
| Examples | String wave, light, ripples | Sound, P-seismic waves, Slinky push |
| Possible in fluids? | Surface waves only (need elasticity of shear) | Always (only need bulk elasticity) |
| Polarisation? | Yes (e.g. polaroid filter) | No |
14.3 Displacement Relation in a Progressive Wave
Consider a sinusoidal transverse wave travelling in the +x direction with amplitude a, period T, and wavelength λ. The displacement y of a particle at position x and time t is:
Progressive wave equation:
\[y(x,t)=a\sin(kx-\omega t+\phi)\]
where:
- a = amplitude (maximum displacement)
- k = angular wave number = 2π/λ (rad/m)
- ω = angular frequency = 2π/T = 2πν (rad/s)
- φ = initial phase (rad)
The wave moves with phase velocity:
\[v = \frac{\omega}{k} = \nu\,\lambda\]
This fundamental relation \(v=\nu\lambda\) connects the speed of any wave to its frequency and wavelength.
14.3.1 Period, Frequency and Phase
The frequency ν is the number of oscillations per second, related to period by \(\nu=1/T\). The argument \((kx-\omega t+\phi)\) is called the phase of the wave.
14.3.2 Wave Speed v
For a fixed point on the wave (constant phase), \(kx - \omega t = \) constant. Differentiating: \(v=\dfrac{dx}{dt}=\dfrac{\omega}{k}\).
Interactive Simulation: Wavelength–Frequency Explorer
Adjust frequency and wavelength to see speed update. Notice they trade off when speed is fixed.
Speed v = ν λ = 5.0 m/s
Worked Example 1: Identify wave parameters
A transverse wave on a rope is described by y(x,t) = 0.04 sin(15x − 50t) m. Find (a) amplitude, (b) wavelength, (c) frequency, (d) wave speed.
Compare with y = a sin(kx − ωt):
(a) Amplitude a = 0.04 m.
(b) k = 15 rad/m ⇒ λ = 2π/k = 2π/15 ≈ 0.419 m.
(c) ω = 50 rad/s ⇒ ν = ω/2π ≈ 7.96 Hz.
(d) v = ω/k = 50/15 ≈ 3.33 m/s.
(a) Amplitude a = 0.04 m.
(b) k = 15 rad/m ⇒ λ = 2π/k = 2π/15 ≈ 0.419 m.
(c) ω = 50 rad/s ⇒ ν = ω/2π ≈ 7.96 Hz.
(d) v = ω/k = 50/15 ≈ 3.33 m/s.
Worked Example 2: Speed of sound from frequency and wavelength
A loudspeaker emits a 440 Hz tone (musical A). In air it has wavelength 78 cm. Find the speed of sound.
\[v = \nu\lambda = 440\times 0.78 = \boxed{343\,\text{m/s}}\]
This is the standard speed of sound in air at 20 °C — matches our expectation.
Worked Example 3: Phase difference
Two points on a progressive wave are separated by 60 cm along the direction of propagation. If the wavelength is 80 cm, what is the phase difference between the two points?
\[\Delta\phi = k\cdot\Delta x = \frac{2\pi}{\lambda}\cdot\Delta x = \frac{2\pi}{0.80}\times 0.60\]
\[=\frac{3\pi}{2}\,\text{rad}=\boxed{270°}\]
Equivalently, the two points are 3/4 of a wavelength apart.
Activity 14.1 — Slinky WavesL3 Apply
Materials: Long slinky (~3 m), tape (marker), partner.
- Stretch the slinky between two students. Mark one coil with tape.
- Give a quick sideways flick at one end — observe a transverse pulse.
- Now push and pull along the slinky's axis — observe a longitudinal pulse with visible compressions.
- For each type, watch what the marked coil does.
Predict: Will the marked coil travel from one end to the other along with the wave?
The marked coil oscillates about its mean position but does NOT travel along with the wave. The wave (energy) propagates along the slinky, but each coil only oscillates locally — exactly the defining feature of wave motion.
Competency-Based Questions
A music recording engineer is monitoring frequencies in a recording studio. She uses a 1024-sample audio spectrum analyser to identify harmonics. The room walls reflect sound, and she needs to understand wavelength behaviour for different musical notes.
Q1. Sound waves in air are:L1 Remember
Answer: (b) Longitudinal. Air has no shear elasticity, so only compression-rarefaction (longitudinal) sound can propagate.
Q2. A 256-Hz tuning fork is sounded. If the speed of sound is 340 m/s, find the wavelength.L3 Apply
λ = v/ν = 340/256 ≈ 1.33 m. This is why low-pitched sounds wrap easily around obstacles (diffraction) — their wavelengths are comparable to door/room sizes.
Q3. True/False: When a sound wave travels from air into water, the frequency changes but wavelength stays the same.L5 Evaluate
FALSE. Frequency is set by the source and does NOT change across media. Speed changes (sound in water ≈ 1500 m/s vs 340 m/s in air), so wavelength changes correspondingly: λ_water = v_water/ν.
Q4. Fill in the blank: The phase difference between two points on a wave separated by a half-wavelength is ____ radians.L2 Understand
π radians (180°). Δφ = (2π/λ)·(λ/2) = π. Half-wavelength shift puts the two points in anti-phase.
Q5. HOT: Design an experiment to demonstrate that water waves are neither purely transverse nor purely longitudinal.L6 Create
Sample design: Float a small piece of cork on a ripple tank. Generate surface waves at one end. Observe and track the cork's motion using a video frame-by-frame. The cork traces nearly circular orbits — moving forward at the crest, backward at the trough, up and down between. This shows both transverse and longitudinal components combined, characteristic of surface gravity waves. Deep-water orbits are circles; shallow-water orbits are ellipses, flattening as depth decreases — explaining wave-breaking on beaches.
Assertion–Reason Questions
(A) Both true, R explains A. (B) Both true, R does NOT explain A. (C) A true, R false. (D) A false, R true.
A: Sound waves cannot travel through vacuum.
R: Sound is a longitudinal wave that requires a material medium for propagation.
(A). Both true; R correctly explains A. This is why space is silent.
A: Light is a transverse wave but sound is a longitudinal wave.
R: Only transverse waves can be polarised.
(B). Both true, but R is a consequence, not the cause. The cause is that EM fields are transverse to propagation; sound in air can only be longitudinal because air can't support shear.
A: The wave speed v = νλ is the same in all media for a given source.
R: Frequency depends only on the source, not the medium.
(D). A is FALSE — speed varies with the medium. R is TRUE. When v changes, λ changes proportionally so the formula holds, but v itself is not universal.
Frequently Asked Questions - Transverse Longitudinal Waves
What is the main concept covered in Transverse Longitudinal Waves?
In NCERT Class 11 Physics Chapter 14 (Waves), "Transverse Longitudinal Waves" covers core principles and equations needed for board exam success. The MyAiSchool lesson explains the topic with definitions, derivations, worked examples, and interactive simulations. Key formulas and dimensional analysis are included to build conceptual depth and problem-solving skills aligned with the CBSE 2025-26 syllabus.
How is Transverse Longitudinal Waves useful in real-life applications?
Real-life applications of Transverse Longitudinal Waves from NCERT Class 11 Physics Chapter 14 include engineering design, satellite mechanics, sports biomechanics, transportation safety, and electrical/electronic devices. The MyAiSchool lesson links every concept to a tangible example so students see physics as a problem-solving framework for the physical world, not as abstract formulas.
What are the key formulas in Transverse Longitudinal Waves?
Key formulas in Transverse Longitudinal Waves (NCERT Class 11 Physics Chapter 14 Waves) are derived step-by-step in the MyAiSchool lesson. Students should memorize the final formula AND understand its derivation for full board marks. Each formula is listed with its dimensional formula, SI unit, applicability range, and common pitfalls. The Summary section at the end of each part includes a quick-reference formula card.
How does this part connect to other parts of Chapter 14?
NCERT Class 11 Physics Chapter 14 (Waves) is structured so each part builds on the previous one. Transverse Longitudinal Waves connects directly to neighbouring parts via shared definitions, units, and methodology. The MyAiSchool lesson cross-references related concepts with internal links so students can navigate the whole chapter as one connected story rather than disconnected fragments.
What types of CBSE board questions come from Transverse Longitudinal Waves?
CBSE board questions from Transverse Longitudinal Waves typically include: (1) 1-mark MCQs on definitions and formulas, (2) 2-mark short-answer derivations or applications, (3) 3-mark numerical problems with units, (4) 5-mark long-answer derivations followed by application. The MyAiSchool lesson tags each Competency-Based Question (CBQ) with Bloom level (L1-L6) so students know how to study for each weight.
How can students use the interactive simulation effectively?
The interactive simulation in the Transverse Longitudinal Waves lesson allows students to adjust input parameters (sliders or selectors) and see physical quantities update in real time. To use it effectively: (1) try extreme values to understand limiting cases, (2) compare with the analytical formula, (3) check unit consistency, (4) test special configurations from worked examples. The simulation reinforces conceptual intuition that pure formula manipulation cannot.
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