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 = 1.328 mv = 340 m/sf = ?

A sound wave in air travels at 340 m/s with a wavelength of 1.328 m. Find its frequency f.

λ = 1.328 mv = 340 m/s
f = Hz
2.Easy
v = 2 × 10⁸ m/s

Light travels at 2 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 2 × 10⁸ m/sc = 3.00 × 10⁸ m/s
n =
3.Medium
SO20 m/sf = 300 Hz

An observer moves at 20 m/s towards a stationary source of 300 Hz. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 300 Hzv = 343 m/svo = 20 m/s
f′ = Hz
4.Medium
FFdo​ = 6 cmf = 15 cm

An object stands 6 cm in front of a thin converging lens with a focal length of 15 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 = 15 cm
di = cm
5.Hard
λ = 550 nma = 0.08 mm

Light of wavelength 550 nm passes through a single slit 0.08 mm wide. Find the angle θ1 of dark fringe number 1 from the straight-through direction.

λ = 550 nma = 0.08 mmm = 1
θ1 = °
6.Hard
θn1​ = 1.48n2​ = 1.38n0​ = 1.00

An optical fibre has a core with n₁ = 1.48 and a cladding with n₂ = 1.38. Find its numerical aperture NA.

n1 = 1.48n2 = 1.38
NA =

Answer key

  1. 1. f = 256 Hz
  2. 2. n = 1.5
  3. 3. f′ = 317.5 Hz
  4. 4. di = −10 cm
  5. 5. θ1 = 0.3939 °
  6. 6. NA = 0.5348

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