Fourier Analysis and the Wave Packet · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Waves built from waves

Science · Waves, Light & Sound · ages 21-22
Name ______________________   Date ____________

  1. When waves meet, how do their disturbances combine?

    • They cancel no matter what
    • They add point by point
    • The taller one erases the smaller

  2. What is a repeating shape made of in Fourier analysis?

    • A sum of sines at whole multiples of a base frequency
    • A single sine at the base frequency
    • A product of unrelated noises

  3. Adding more harmonics makes a square wave sum match better.

    Circle one:   True   False

  4. Why does a narrow channel smear sharp pulses?

    • It must carry every frequency, and it drops the fast ones
    • It amplifies the slow parts too much
    • It adds random new frequencies

  5. Two pulses carry the same shape but one is half as long. What does it need?

    • Half the frequency range
    • The same frequency range
    • Twice the frequency range

  6. Two identical waves arrive exactly in phase. What results?

    • Pure constructive interference with doubled amplitude
    • Complete cancellation to nothing
    • A wave at half the wavelength

  7. A student claims one sine wave alone equals a square wave. What is wrong?

    • Sines cannot be added together
    • A square wave needs many harmonics to form its jumps
    • Square waves contain no frequencies at all

  8. An engineer doubles a link speed with sharper pulses but keeps the old bandwidth. What happens?

    • The pulses arrive sharper than before
    • Nothing changes in the received signal
    • The channel rounds off the new fast edges
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Waves built from waves W1-mt_1ZaojWUZEw-s1

  1. They add point by point · Superposition adds disturbances wherever waves overlap.
  2. A sum of sines at whole multiples of a base frequency · Harmonics at whole multiples stack into any repeating shape.
  3. True · Each term sharpens the corners toward the true jumps.
  4. It must carry every frequency, and it drops the fast ones · Missing high frequencies rounds off the fast changes.
  5. Twice the frequency range · Squeezing in time spreads the signal in frequency.
  6. Pure constructive interference with doubled amplitude · Aligned crests add, doubling the height at the same wavelength.
  7. A square wave needs many harmonics to form its jumps · One term gives a smooth wave; the jumps need the full stack.
  8. The channel rounds off the new fast edges · Sharper pulses need wider bands, which the old channel lacks.
Worksheet · LightMySky