A wave pulse is propagating on a long string along the length taken as +x axis. Shape of the string
at $$t=0$$ is given by $$y=\frac{1}{x^2+8x+19}$$ and at $$t=2\ \sec$$ the shape is $$y=\frac{1}{x^2+3}$$. find the speed of wave on string
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Waves is a high-weightage and conceptually demanding chapter in JEE Physics that describes how disturbances travel through media. It covers mechanical waves, sound, superposition, standing waves, and the Doppler effect topics that recur in JEE Main and feature prominently in JEE Advanced. Because waves blend equations with physical reasoning about interference and resonance, JEE Waves questions are an essential part of every aspirant's preparation. This chapter covers the wave equation, travelling and standing waves, superposition and interference, beats, vibrations in strings and air columns, and the Doppler effect for sound. JEE Main tests wave parameters, resonance, and Doppler problems, while JEE Advanced often combines these with deeper reasoning about phase and harmonics. Practising topic-wise JEE Questions help you handle standing-wave and Doppler problems with clarity and speed. A strong grasp of waves also supports wave optics, where the same superposition and interference principles reappear in the context of light.
A wave pulse is propagating on a long string along the length taken as +x axis. Shape of the string
at $$t=0$$ is given by $$y=\frac{1}{x^2+8x+19}$$ and at $$t=2\ \sec$$ the shape is $$y=\frac{1}{x^2+3}$$. find the speed of wave on string
At $$t=0$$, the shape of the pulse is
$$y=\frac{1}{x^2+8x+19}=\frac{1}{(x+4)^2+3}$$
At $$t=2\,\text{s}$$, the shape is
$$y=\frac{1}{x^2+3}$$
Thus, the pulse has shifted from $$x=-4$$ to $$x=0$$, i.e. it has moved $$4\,\text{m}$$ in the $$+x$$ direction.
Hence, the speed of the wave is
$$v=\frac{\text{distance travelled}}{\text{time taken}}=\frac{4}{2}=2\,\text{m s}^{-1}$$
Therefore, $${v=2\,\text{m s}^{-1}}$$
Hence, the correct option is C.
Parameter | Details |
|---|---|
Topic Name | Waves |
Subject | Physics |
JEE Main Weightage | ~3–5% (1–2 questions on average) |
JEE Advanced Weightage | ~4–6% (often in combined problems) |
Difficulty Level | Moderate to High |
Important Concepts | Wave Equation, Standing Waves, Superposition, Beats, Resonance, Doppler Effect |
Recommended Practice Level | High – attempt 60+ mixed problems |
Concept | Importance | Difficulty Level | Frequently Asked In |
|---|---|---|---|
Wave Equation & Parameters | Very High | Moderate | JEE Main & Advanced |
Superposition & Interference | Very High | Moderate–High | JEE Main & Advanced |
Standing Waves in Strings | Very High | Moderate–High | JEE Main & Advanced |
Standing Waves in Air Columns | High | Moderate | JEE Main & Advanced |
Beats | High | Moderate | JEE Main |
Doppler Effect (Sound) | Very High | Moderate–High | JEE Main & Advanced |
Concept learning: Understand the wave equation and the meaning of amplitude, wavelength, frequency, and phase. Master superposition as the principle behind interference, beats, and standing waves.
Formula revision: Keep relations for wave speed, standing-wave harmonics in strings and pipes, beat frequency, and the Doppler effect handy. Organised JEE Study Material helps you keep these formulas and harmonic patterns in one place for quick revision.
Problem-solving techniques: For standing waves, identify open and closed boundaries to determine allowed harmonics. For Doppler problems, carefully assign signs to source and observer velocities based on direction.
Common mistakes: Sign errors in the Doppler formula, confusing harmonics in open versus closed pipes, mishandling phase difference in interference, and unit errors in wave speed.
Exam strategy: Solve direct wave-parameter and beat questions first, then attempt standing-wave and Doppler problems that require careful setup.
Exam | Average Questions | Expected Marks |
|---|---|---|
JEE Main | 1–2 | 4–8 |
JEE Advanced | 1–2 | 4–8 |
Waves is a steady contributor in JEE Main through resonance, beats, and Doppler questions. In JEE Advanced, it often appears in combined problems demanding careful phase and harmonic analysis.
Reinforcing these methods with a timed JEE Mock Test helps you handle standing-wave and Doppler questions efficiently under pressure.
JEE Waves questions cover topics such as the wave equation, standing waves, superposition, interference, beats, resonance, and the Doppler effect in both JEE Main and JEE Advanced.
Yes. Waves is a high-weightage chapter that typically contributes 1–2 questions in JEE Main and serves as a foundation for wave optics and other wave-based concepts.
Standing waves, resonance, and the Doppler effect are among the most frequently tested concepts. Questions involving organ pipes and harmonic frequencies are also common.
The chapter is generally considered moderate to high in difficulty. Students often find Doppler-effect and standing-wave problems challenging because they require careful interpretation and setup.
JEE Main usually includes 1–2 questions from Waves, while JEE Advanced often asks 1–2 conceptual or multi-topic problems involving wave phenomena.
Solve topic-wise previous year questions, focus on standing-wave patterns, resonance, and Doppler-effect problems, and regularly attempt timed mock tests.
Common mistakes include sign errors in the Doppler-effect formula, confusion between open and closed pipe harmonics, and incorrect phase-difference calculations in interference problems.
Waves forms the basis for understanding many physical phenomena and helps students tackle questions from sound waves, wave optics, oscillations, and related topics throughout the JEE syllabus.
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