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
λ = 3.43 mv = ?f = 100 Hz

A sound wave in air has a frequency of 100 Hz and a wavelength of 3.43 m. Find its speed v.

f = 100 Hzλ = 3.43 m
v = m/s
2.Easy
λ = 1.5 mv = ?f = 0.8 Hz

A water wave has a frequency of 0.8 Hz and a wavelength of 1.5 m. Find its speed v.

f = 0.8 Hzλ = 1.5 m
v = m/s
3.Medium
FFdo​ = 60 cmf = 15 cm

An object stands 60 cm in front of a thin converging lens with a focal length of 15 cm. Find the magnification m (negative for an inverted image).

do = 60 cmf = 15 cm
m =
4.Medium
FFdo​ = 4 cmf = −20 cm

An object stands 4 cm in front of a thin diverging lens with a focal length of 20 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 = 4 cmf = −20 cm
di = cm
5.Hard
λ = ?23.2°

A grating with 600 lines per millimetre shows the order-1 maximum of a spectral line at 23.2° from the straight-through direction. Find the wavelength λ of the line.

N = 600 mm⁻¹θ1 = 23.2°m = 1
λ = nm
6.Hard
θn1​ = 1.5n2​ = 1.4n0​ = 1.00

An optical fibre has a core with n₁ = 1.5 and a cladding with n₂ = 1.4. Find its numerical aperture NA.

n1 = 1.5n2 = 1.4
NA =

Answer key

  1. 1. v = 343 m/s
  2. 2. v = 1.2 m/s
  3. 3. m = −0.3333
  4. 4. di = −3.333 cm
  5. 5. λ = 656.6 nm
  6. 6. NA = 0.5385

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