Waves, sound & optics worksheet with answers

Free printable Waves, sound & optics worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
20°θ₂ = ?glycerol, n1​ = 1.47acrylic, n2​ = 1.49

A light ray in glycerol (n = 1.47) strikes a flat boundary with acrylic (n = 1.49) at 20° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.47n2 = 1.49θ1 = 20°
θ2 = °
2.Easy
v = 2.04 × 10⁸ m/s

Light travels at 2.04 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 2.04 × 10⁸ m/sc = 3.00 × 10⁸ m/s
n =
3.Medium
θc = ?90°glycerol, n1​ = 1.47air, n2​ = 1.00

Light travels in glycerol (n = 1.47) towards a flat boundary with air (n = 1.00). Find the critical angle θc beyond which it is totally reflected.

n1 = 1.47n2 = 1.00
θc = °
4.Medium
S15 m/sOf = 300 Hz

A source of 300 Hz moves at 15 m/s towards a stationary observer. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 300 Hzv = 343 m/svs = 15 m/s
f′ = Hz
5.Hard
λ = 550 nmd = 0.4 mmL = 1 my = ?

Light of wavelength 550 nm falls on two slits 0.4 mm apart. The screen is 1 m away. Find the distance y3 from the central bright fringe to bright fringe number 3.

λ = 550 nmd = 0.4 mmL = 1 mm = 3
y3 = mm
6.Hard
λ = 633 nma = 0.2 mm

Light of wavelength 633 nm passes through a single slit 0.2 mm wide. Find the angle θ1 of dark fringe number 1 from the straight-through direction.

λ = 633 nma = 0.2 mmm = 1
θ1 = °

Answer key

  1. 1. θ2 = 19.72 °
  2. 2. n = 1.471
  3. 3. θc = 42.86 °
  4. 4. f′ = 313.7 Hz
  5. 5. y3 = 4.125 mm
  6. 6. θ1 = 0.1813 °

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