Phasor Addition and the Mathematics of Interference · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Adding waves with arrows

Science · Waves, Light & Sound · ages 19-21
Name ______________________   Date ____________

  1. The resultant amplitude doubles. What happens to the brightness?

    • It grows fourfold
    • It doubles
    • It stays the same

  2. Two equal waves arrive exactly in step. What do their arrows do?

    • They point opposite ways and cancel
    • They point the same way and add to double length
    • They curl into a closed triangle

  3. Two slits are spaced d apart. When is a bright fringe seen at angle theta?

    • When the screen is moved closer
    • When d sin theta is half a wavelength
    • When d sin theta is a whole number of wavelengths

  4. The screen is moved twice as far from two slits. What happens to the fringe spacing?

    • It halves
    • It doubles
    • It stays the same

  5. Three equal waves arrive in step, each of amplitude 2 units. Type the resultant amplitude.

    Answer: ______________

  6. Why do more slits make the bright fringes sharper?

    • Each slit gets brighter than before
    • The wavelength gets shorter
    • The arrows align fully only at main maxima and curl toward zero elsewhere

  7. A student claims dark fringes prove that light energy disappears. What is the best reply?

    • The dark zone energy is piled into the bright fringes
    • The slits absorb the missing energy
    • The wavelength changes in the dark zones

  8. Three equal waves with phase steps of 120 degrees add to zero.

    Circle one:   True   False

LightMySky · lightmysky.comW1-mt_dxh7HHbIUw-s1

Answer key

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

Adding waves with arrows W1-mt_dxh7HHbIUw-s1

  1. It grows fourfold · Brightness goes as amplitude squared, and two squared is four.
  2. They point the same way and add to double length · In-step arrows share one direction, so their lengths simply add.
  3. When d sin theta is a whole number of wavelengths · Whole wavelength path gaps arrive in step and build bright fringes.
  4. It doubles · Spacing is wavelength times screen distance over slit spacing, so doubling the distance doubles the spacing.
  5. 6 · Three in-line arrows of length 2 join to a single arrow of length 6.
  6. The arrows align fully only at main maxima and curl toward zero elsewhere · Full alignment happens only at the main maxima, while elsewhere the arrows curl away to nothing.
  7. The dark zone energy is piled into the bright fringes · Cancellation in dark zones is balanced by extra brightness at the maxima.
  8. True · Their arrows close into a triangle, so the resultant has zero length.
Worksheet · LightMySky