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
70°θ₂ = ?acrylic, n1​ = 1.49crown glass, n2​ = 1.50

A light ray in acrylic (n = 1.49) strikes a flat boundary with crown glass (n = 1.50) at 70° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.49n2 = 1.50θ1 = 70°
θ2 = °
2.Easy
L = 1 m

A string of length 1 m and mass 4 g is stretched with a tension of 20 N. Find the speed v of transverse waves on it.

L = 1 mm = 4 gT = 20 N
v = m/s
3.Medium
S34 m/sO10 m/sf = 500 Hz

A source of 500 Hz moving at 34 m/s and an observer moving at 10 m/s move away from each other. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 500 Hzv = 343 m/svs = 34 m/svo = 10 m/s
f′ = Hz
4.Medium
FFdo​ = 8 cmf = 12 cm

An object stands 8 cm in front of a thin converging lens with a focal length of 12 cm. Find the image distance di. Use the sign convention 1/f = 1/do + 1/di (f < 0 for a diverging lens, di < 0 for a virtual image).

do = 8 cmf = 12 cm
di = cm
5.Hard
Fdo​ = 5 cmR = 60 cm

An object is 5 cm in front of a concave mirror with a radius of curvature of 60 cm. Find the magnification m (negative for an inverted image).

do = 5 cmR = 60 cm
m =
6.Hard
λ = 450 nmd = 0.5 mmL = 1.2 m

Light of wavelength 450 nm falls on two slits 0.5 mm apart. The screen is 1.2 m away. Find the spacing Δy between neighbouring bright fringes.

λ = 450 nmd = 0.5 mmL = 1.2 m
Δy = mm

Answer key

  1. 1. θ2 = 68.98 °
  2. 2. v = 70.71 m/s
  3. 3. f′ = 441.6 Hz
  4. 4. di = −24 cm
  5. 5. m = 1.2
  6. 6. Δy = 1.08 mm

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