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
25°θ₂ = ?water, n1​ = 1.33acrylic, n2​ = 1.49

A light ray in water (n = 1.33) strikes a flat boundary with acrylic (n = 1.49) at 25° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.33n2 = 1.49θ1 = 25°
θ2 = °
2.Easy
λ = 4 mv = 2 m/sf = ?

A water wave travels at 2 m/s with a wavelength of 4 m. Find its frequency f.

λ = 4 mv = 2 m/s
f = Hz
3.Medium
45°90°n1​ = ?ethanol, n2​ = 1.36

Light inside a transparent block is totally reflected at the boundary with ethanol (n = 1.36) for every angle of incidence above 45°. Find the refractive index n1 of the block.

θc = 45°n2 = 1.36
n1 =
4.Medium
L = ?n = 5

A pipe open at both ends must have its harmonic number 5 at 1715 Hz. The speed of sound is 343 m/s. Find the length L of the pipe.

v = 343 m/sn = 5f5 = 1715 Hz
L = m
5.Hard
SO15 m/sf = 40 kHz

A parking sensor at rest sends ultrasound of 40 kHz towards a car that moves away at 15 m/s. Find the frequency f″ of the echo received back at the sensor (speed of sound 343 m/s).

f = 40 kHzu = 15 m/sv = 343 m/s
f″ = Hz
6.Hard
λ = 405 nmθ

A diffraction grating has 800 lines per millimetre. Light of wavelength 405 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 800 mm⁻¹λ = 405 nm
mmax =

Answer key

  1. 1. θ2 = 22.16 °
  2. 2. f = 0.5 Hz
  3. 3. n1 = 1.923
  4. 4. L = 0.5 m
  5. 5. f″ = 36648 Hz
  6. 6. mmax = 3

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