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 = 1.24 × 10⁸ m/s

Light travels at 1.24 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 1.24 × 10⁸ m/sc = 3.00 × 10⁸ m/s
n =
2.Easy
λ = ?v = 1.5 m/sf = 0.2 Hz

A water wave has a frequency of 0.2 Hz and travels at 1.5 m/s. Find its wavelength λ.

f = 0.2 Hzv = 1.5 m/s
λ = m
3.Medium
L = ?n = 5

A pipe closed at one end must have its harmonic number 5 at 1072 Hz. The speed of sound is 343 m/s. Find the length L of the pipe.

v = 343 m/sn = 5f5 = 1072 Hz
L = m
4.Medium
FFdo​ = 6 cmf = 10 cm

An object stands 6 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 = 6 cmf = 10 cm
di = cm
5.Hard
λ = ?d = 0.2 mmL = 1.5 m15.96 mm

Two slits 0.2 mm apart are lit with monochromatic light. On a screen 1.5 m away, bright fringe number 4 lies 15.96 mm from the central fringe. Find the wavelength λ.

d = 0.2 mmL = 1.5 my4 = 15.96 mmm = 4
λ = nm
6.Hard
θa​ = ?n1​ = 1.5n2​ = 1.42n0​ = 1.00

An optical fibre has a core with n₁ = 1.5 and a cladding with n₂ = 1.42. Find the largest angle θa to the fibre axis at which light from air can enter the end of the fibre and still be guided by total internal reflection.

n1 = 1.5n2 = 1.42n0 = 1.00
θa = °

Answer key

  1. 1. n = 2.419
  2. 2. λ = 7.5 m
  3. 3. L = 0.4 m
  4. 4. di = −15 cm
  5. 5. λ = 532 nm
  6. 6. θa = 28.9 °

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