Irodov Part 4 Oscillations and Waves — What to Solve for JEE
A section-by-section map of Part Four of I.E. Irodov’s Problems in General Physics, checked against the JEE Main and JEE Advanced syllabuses.
Part Four has the best ratio in the book: 224 problems, of which about 168 are worth attempting, and 132 sit in sections that are wholly in scope. It also contains the largest fully in-scope section anywhere in Irodov — 4.1 Mechanical Oscillations, at 93 problems.
It is also the part where the difference between the two exams matters most. The JEE Main syllabus carries no free, forced or damped oscillations, no resonance outside a.c. circuits, and no Doppler effect in sound. All three are on the JEE Advanced syllabus. A Main candidate loses more of this part than of any other; an Advanced candidate should treat it as a priority.
Key insight. Irodov treats oscillation as a differential equation with a solution, not as a formula to substitute into. Once you can write the equation of motion and read the frequency off it, the whole part becomes one technique applied to springs, pendulums, liquid columns, circuits and rotating bodies in turn — which is exactly how Advanced likes to ask it.
The sections at a glance
| Section | Problems | Count | Verdict | Roughly in scope |
|---|---|---|---|---|
| 4.1 Mechanical Oscillations | 4.1–4.93 | 93 | Solve (Advanced) | 93 |
| 4.2 Electric Oscillations | 4.94–4.149 | 56 | Mostly solve | ~36 |
| 4.3 Elastic Waves. Acoustics | 4.150–4.188 | 39 | Solve | 39 |
| 4.4 Electromagnetic Waves. Radiation | 4.189–4.224 | 36 | Skip entirely | 0 |
Section 4.1 — Mechanical Oscillations
Ninety-three problems, and for an Advanced candidate all of them are in scope. The syllabus names linear and angular simple harmonic motion, and — explicitly — forced and damped oscillation and resonance. This is the single largest block of fully usable problems in Irodov.
The section keeps returning to three things: deriving the equation of motion for a system that is not a spring and a block, so that the restoring term has to be found rather than recalled; combining oscillations, including perpendicular ones; and damped and driven motion, where the amplitude depends on how far the driving frequency sits from resonance.
If you are sitting JEE Main only, stop at simple harmonic motion. Damped and forced oscillations and resonance are not on the Main syllabus — its only mention of resonance is in a.c. circuits — and they are a substantial share of this section.
Before you start it: Oscillations.
Section 4.2 — Electric Oscillations
Fifty-six problems, of which about thirty-six are usable. LC and LCR circuits with direct and alternating sources are on the syllabus, and the damped and driven electrical problems inherit the same entry that covers their mechanical counterparts.
Solve the free, damped and driven oscillation problems, the resonance ones, and the alternating-current circuit problems. Skip the material on quality factor pushed beyond a definition — the quality factor is on neither syllabus — and anything treating an oscillating circuit as a radiating system, which belongs to 4.4.
Do this section straight after 4.1. The mathematics is identical and seeing the same differential equation describe a mass on a spring and a charge in a circuit is the point Irodov is making.
Before you start it: Alternating Current.
Section 4.3 — Elastic Waves. Acoustics
Thirty-nine problems, all in scope for Advanced. Wave motion, longitudinal and transverse waves, superposition, progressive and standing waves, vibrations of strings and air columns, the speed of sound in gases, beats and the Doppler effect — every one of those is named on the Advanced syllabus.
If you are sitting JEE Main only, the Doppler effect in sound is not on your syllabus, which takes out a slice of the section. Beats are on it — the Main syllabus names them in its oscillations and waves unit — despite being listed as deleted by most of the summaries circulating online.
Acoustic intensity and the decibel scale appear in Irodov and on neither syllabus; they are easy to spot and easy to skip.
Before you start it: Waves.
Section 4.4 — Electromagnetic Waves. Radiation
Skip the entire section. Thirty-six problems on the Poynting vector, radiated power and dipole radiation. Both syllabuses carry only the characteristics of electromagnetic waves and the spectrum, which this section never stops to cover.
Instead: Electromagnetic Waves covers everything the exam asks on the topic.
Common mistakes with Part Four
Skipping 4.1 on the belief that damped and forced oscillations are off the syllabus. They are — for Main. For Advanced the syllabus names “forced and damped oscillation (in one dimension), resonance” in those words, and acting on the wrong one of those two facts costs you the largest fully usable section in the book. This is the correction that mattered most when this guide was checked against the syllabuses.
Treating 4.2 as an electricity topic to be done later. It is the same mathematics as 4.1 and should follow it immediately, while the method is fresh.
Doing 4.4 because it is short and comes next. Thirty-six problems, none of them askable.
Learning standing waves as string formulae. Irodov asks about boundary conditions — which end is free, which is fixed, what that does to the allowed wavelengths. Memorised formulae fail the moment the boundary changes.
What to read next
- Part 5 — Optics, the part with no fully in-scope section at all
- Part 3 — Electrodynamics, which pairs with 4.2
- Should you solve Irodov at all?