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
25°θ₂ = ?ethanol, n1​ = 1.36flint glass, n2​ = 1.62

A light ray in ethanol (n = 1.36) strikes a flat boundary with flint glass (n = 1.62) at 25° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.36n2 = 1.62θ1 = 25°
θ2 = °
2.Easy
Pβ = 55 dB

The sound intensity level at a point is 55 dB. Find the sound intensity I.

β = 55 dBI0 = 10⁻¹² W/m²
I = µW/m²
3.Medium
θc = ?90°glycerol, n1​ = 1.47water, n2​ = 1.33

Light travels in glycerol (n = 1.47) towards a flat boundary with water (n = 1.33). Find the critical angle θc beyond which it is totally reflected.

n1 = 1.47n2 = 1.33
θc = °
4.Medium
L = 1.2 mn = 3

A string fixed at both ends is 1.2 m long; waves travel on it at 100 m/s. Find the frequency f3 of its harmonic number 3.

v = 100 m/sn = 3L = 1.2 m
f3 = Hz
5.Hard
Fdo​ = 8 cmR = 20 cm

An object is 8 cm in front of a concave mirror with a radius of curvature of 20 cm. Find the magnification m (negative for an inverted image).

do = 8 cmR = 20 cm
m =
6.Hard
λ = 656 nmθ

A diffraction grating has 1200 lines per millimetre. Light of wavelength 656 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 1200 mm⁻¹λ = 656 nm
mmax =

Answer key

  1. 1. θ2 = 20.78 °
  2. 2. I = 0.3162 µW/m²
  3. 3. θc = 64.79 °
  4. 4. f3 = 125 Hz
  5. 5. m = 5
  6. 6. mmax = 1

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