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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
L = 0.5 m

A string of length 0.5 m and mass 4 g is stretched with a tension of 250 N. Find the speed v of transverse waves on it.

L = 0.5 mm = 4 gT = 250 N
v = m/s
2.Easy
L = 1 m

A string of length 1 m and mass 8 g is stretched with a tension of 120 N. Find the speed v of transverse waves on it.

L = 1 mm = 8 gT = 120 N
v = m/s
3.Medium
θc = ?90°ethanol, n1​ = 1.36air, n2​ = 1.00

Light travels in ethanol (n = 1.36) towards a flat boundary with air (n = 1.00). Find the critical angle θc beyond which it is totally reflected.

n1 = 1.36n2 = 1.00
θc = °
4.Medium
FF5 cmdo​ = 60 cmf = −8 cm

An object 5 cm tall stands 60 cm in front of a thin diverging lens with a focal length of 8 cm. Find the image height hi (negative for an inverted image).

ho = 5 cmdo = 60 cmf = −8 cm
hi = cm
5.Hard
f1​ = 10 cmf2​ = −20 cm30 cm25 cm

Two thin lenses share an axis, 25 cm apart: lens 1 with f₁ = 10 cm and lens 2 with f₂ = −20 cm. An object stands 30 cm in front of lens 1. Find the position di2 of the final image measured from lens 2 (positive beyond lens 2, real-is-positive convention).

f1 = 10 cmf2 = −20 cms = 25 cmdo = 30 cm
di2 = cm
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. v = 176.8 m/s
  2. 2. v = 122.5 m/s
  3. 3. θc = 47.33 °
  4. 4. hi = 0.5882 cm
  5. 5. di2 = −6.667 cm
  6. 6. NA = 0.5348

Full step-by-step solutions: practise this topic on examproblems.com.