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
v = 2.21 × 10⁸ m/s

Light travels at 2.21 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 2.21 × 10⁸ m/sc = 3.00 × 10⁸ m/s
n =
2.Easy
λ = ?v = 3 m/sf = 0.8 Hz

A water wave has a frequency of 0.8 Hz and travels at 3 m/s. Find its wavelength λ.

f = 0.8 Hzv = 3 m/s
λ = m
3.Medium
FFdo​ = 60 cmf = 10 cm

An object stands 60 cm in front of a thin converging lens with a focal length of 10 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 = 60 cmf = 10 cm
di = cm
4.Medium
S34 m/sOf = 1200 Hz

A source of 1200 Hz moves at 34 m/s towards a stationary observer. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 1200 Hzv = 343 m/svs = 34 m/s
f′ = Hz
5.Hard
λ = 405 nmθ3​ = ?

Light of wavelength 405 nm falls at right angles on a grating with 800 lines per millimetre. Find the angle θ3 of the order-3 maximum.

N = 800 mm⁻¹λ = 405 nmm = 3
θ3 = °
6.Hard
λ = 600 nmθ1​ = ?

Light of wavelength 600 nm falls at right angles on a grating with 1200 lines per millimetre. Find the angle θ1 of the order-1 maximum.

N = 1200 mm⁻¹λ = 600 nmm = 1
θ1 = °

Answer key

  1. 1. n = 1.357
  2. 2. λ = 3.75 m
  3. 3. di = 12 cm
  4. 4. f′ = 1332 Hz
  5. 5. θ3 = 76.41 °
  6. 6. θ1 = 46.05 °

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