E ExamMaster

CBSE Class 11 · Physics

Waves

Official NCERT chapter from Physics Part I–II (book code keph1). ExamMaster notes are original teaching at CBSE Class 11 depth.

This lesson follows the official chapter “Waves” in Physics Part I–II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.

  • CBSE Class 11
  • Medium level
  • 8 concepts

1Transverse and longitudinal waves

Transverse waves move the bits perpendicular to the travel (a string-wiggle); longitudinal waves move them along the travel (a sound-compress). A slinky can show both as taught. Polarisation is a transverse-only story if named. The type is the bit-move, not the leftover “wave” word.

Calling sound transverse because a graph wiggles is a miss.

Figure. A wave is named by how the particles move relative to the travel arrow. Transverse: the ticks are up and down, across the travel. Longitudinal: the same particles bunch and spread along the travel — a compression then a rarefaction. The squares are parcels of the medium, not a drawn circle.

How it works

  1. Name bit-move versus travel-directionPerp or along.
  2. Hang transverse / longitudinalThe type.
  3. Keep sound as longitudinal in air as taughtThis class.

2Displacement relation in a progressive wave

A progressive wave’s displacement is a taught sine of (kx − ωt) or the twin. A snapshot is a sine-in-space; a fixed-x story is a sine-in-time. y=0.02 sin(4πx − 20πt) (SI) names A, k, ω as you read them. A pretty sine with no (kx−ωt) is a doodle.

Using t as if it were x in the snapshot is a mix.

Figure. At one frozen time a travelling wave is just this snapshot: displacement y against position x. The midline is y = 0. The crest is +A and the trough is -A. Later times slide the same shape along x; they do not change A or the wavelength.

How it works

  1. Write y = A sin(kx − ωt) as taughtThe relation.
  2. Read A, λ=2π/k, T=2π/ωThe names.
  3. Keep a snapshot versus a time-trace apartTwo looks.

Read k and ω

In y=0.02 sin(4πx − 20πt) (SI), find λ and T.

  • k=4πλ=2π/k=0.50 m
  • ω=20πT=2π/ω=0.10 s
  • v=λ/T5.0 m/s

Pro tip. Read k and ω from the write; then v=λ/T or ω/k.

3The speed of a travelling wave

The speed of a travelling wave is v = ω/k = λ/T = fλ. On a string, a taught √(T/μ) if named. 0.50 m and 0.10 s is 5.0 m/s. Speed is the pattern’s travel, not a bit’s small jiggle-speed.

Using the jiggle-speed as v is the miss.

Figure. The distance from one crest to the next — here the full x-span — is one wavelength lambda. Frequency f is how many such lengths pass a point each second, so the travel speed is the product v = f lambda. Do not borrow a sound-in-air number; compute v from the f and lambda you were given.

How it works

  1. Name λ and T, or ω and kThe given.
  2. Write v=λ/T or ω/kThe speed.
  3. Keep bits mostly jiggling, the pattern travellingThe wave.

4The principle of superposition of waves

Superposition: overlapping waves add displacements at each point (as taught). Two equal opposite-going waves can make a standing pattern. Superposition is an add, not a collision that deletes energy in the school linear story.

Winner-takes-all at a crossing is not this principle.

Figure. Superposition is a pointwise sum: at each x the net displacement is y1 + y2. These two in-phase waves have the same amplitude, so the solid sum is exactly twice as tall and still one cycle. Out of phase they would cancel; the rule does not change.

How it works

  1. At a point, add the two y’sThe principle.
  2. Read a bigger or a cancel as the sumThe look.
  3. Keep energy as a later honest sentence if taughtAdd first.

5Reflection of waves

Reflection of a wave: a fixed end flips the pulse (as taught); a free end does not. A wave on a string hitting a wall is the flip-story. Reflection is the bounce-job, not every quiet room.

A whisper without a named end-condition is not this heading.

Figure. A rigid end cannot move, so the returning pulse is inverted — the dashed peak points the opposite way and travels back. A free end would return the pulse the same way up. The wall is a boundary condition, not decoration.

How it works

  1. Name the end: fixed or freeThe given.
  2. Say flip or no-flip as taughtThe reflect.
  3. Keep the travel-direction reversedThe bounce.

6Beats

Beats: two close frequencies f1, f2 give a loud-soft at |f1−f2| as taught. 256 Hz and 260 Hz beat at 4 Hz. Beats are a superposition-in-time, not a third instrument. A wide gap is not this slow wax-wane.

Adding 256+260 as the beat is a miss.

Figure. Beats are the slow rise and fall of loudness when two close frequencies share a medium. The fast wiggle is the average frequency; the loud-quiet-loud envelope repeats at |f1 - f2|. Here five and seven cycles sit in the same second, so two beats land in that second.

How it works

  1. Name the two close f’sThe given.
  2. Write |f1−f2| as the beat frequencyThe heading.
  3. Keep them close so the wax is hearable as taughtThis class.

7A definition is a test you can run

Wave / beat is a test: a type, a (kx−ωt), v=fλ, or |f1−f2|. If you only say “wiggle”, you have a heading.

A pond-photo is not the test.

Figure. Before a wave formula is honest you can run this three-step test: name what is measured, name the SI unit, and only then write the relation. Skipping to the sine shape is how y gets treated as a picture instead of a metre of displacement.

How it works

  1. Name type, write, v, or beatThe object.
  2. Give the school sentenceThe test.
  3. Then the word has contentThe definition ran.

8Name the given before the unknown

The given is the sine-write or the two f’s. The unknown is λ, v, or the beat. Copy the 4π as k before you treat it as ω.

Using 20π as k in y=0.02 sin(4πx−20πt) is a silent swap.

Figure. The asked speed is last. Write the frequency and the wavelength with units first; only then form v = f lambda. Starting at the unknown is how a neighbour-chapter formula gets borrowed.

How it works

  1. Copy the write or the two pitchesThe given.
  2. Name λ, T, v, or |f1−f2|The unknown.
  3. Then read k, ω or subtractGiven first.
256 Hz and 260 Hz beat at
  1. 4 Hz
  2. 516 Hz
  3. 258 Hz

|f1−f2|, not the sum.

Notes

  • Mapped to the official NCERT chapter “Waves”. Original teaching only — no textbook sentences.
  • Science here is Physics, Chemistry and Biology ideas at this class, never a language or social-science chapter.

Formulas

  • v=fλ=ω/k
  • λ=2π/k, T=2π/ω
  • beat = |f1−f2|

Recap

Hold these pegs from the official chapter “Waves”. The wording is ExamMaster’s teaching, not a textbook recap.

Transverse and longitudinal waves
Transverse waves move the bits perpendicular to the travel (a string-wiggle); longitudinal waves move them along the travel (a sound-compress).
Displacement relation in a progressive wave
A progressive wave’s displacement is a taught sine of (kx − ωt) or the twin.
The speed of a travelling wave
The speed of a travelling wave is v = ω/k = λ/T = fλ.
The principle of superposition of waves
Superposition: overlapping waves add displacements at each point (as taught).
Reflection of waves
Reflection of a wave: a fixed end flips the pulse (as taught); a free end does not.
Beats
Beats: two close frequencies f1, f2 give a loud-soft at |f1−f2| as taught.

Practise Waves

Reading is free and needs no account. Practice, mocks and progress live in the app.

  • A 4-question practice set that ends the chapter
  • 1 quick check with worked explanations
  • Timed mocks scored with the real marking scheme
  • Readiness tracked per topic, kept on your device
Continue with Google — freeNo card, no trial. Works offline once installed.