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
PI = 1 × 10⁻⁵ W/m²

The sound intensity near a busy street is 1 × 10⁻⁵ W/m². Find the sound intensity level β in decibels.

I = 1 × 10⁻⁵ W/m²I0 = 10⁻¹² W/m²
β = dB
2.Easy
50°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 50° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.33n2 = 1.49θ1 = 50°
θ2 = °
3.Medium
L = 1.5 mn = 2

A string fixed at both ends is 1.5 m long; waves travel on it at 300 m/s. Find the frequency f2 of its harmonic number 2.

v = 300 m/sn = 2L = 1.5 m
f2 = Hz
4.Medium
L = 0.5 mn = 3

A pipe open at both ends is 0.5 m long. The speed of sound is 343 m/s. Find the frequency f3 of its harmonic number 3.

v = 343 m/sn = 3L = 0.5 m
f3 = Hz
5.Hard
λ = 589 nmθ

A diffraction grating has 100 lines per millimetre. Light of wavelength 589 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 100 mm⁻¹λ = 589 nm
mmax =
6.Hard
λ = 450 nmθ

A diffraction grating has 300 lines per millimetre. Light of wavelength 450 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 300 mm⁻¹λ = 450 nm
mmax =

Answer key

  1. 1. β = 70 dB
  2. 2. θ2 = 43.14 °
  3. 3. f2 = 200 Hz
  4. 4. f3 = 1029 Hz
  5. 5. mmax = 16
  6. 6. mmax = 7

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