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 = 3 × 10⁻⁴ W/m²

The sound intensity near a lawn mower is 3 × 10⁻⁴ W/m². Find the sound intensity level β in decibels.

I = 3 × 10⁻⁴ W/m²I0 = 10⁻¹² W/m²
β = dB
2.Easy
λ = 0.1715 mv = 343 m/sf = ?

A sound wave in air travels at 343 m/s with a wavelength of 0.1715 m. Find its frequency f.

λ = 0.1715 mv = 343 m/s
f = kHz
3.Medium
L = 0.8 mn = 5

A pipe closed at one end is 0.8 m long. The speed of sound is 343 m/s. Find the frequency f5 of its harmonic number 5.

v = 343 m/sn = 5L = 0.8 m
f5 = Hz
4.Medium
L = ?n = 1

A pipe closed at one end must have its fundamental (first harmonic) at 172 Hz. The speed of sound is 343 m/s. Find the length L of the pipe.

v = 343 m/sn = 1f1 = 172 Hz
L = m
5.Hard
λ = 633 nma = 0.15 mm

Light of wavelength 633 nm passes through a single slit 0.15 mm wide. Find the angle θ3 of dark fringe number 3 from the straight-through direction.

λ = 633 nma = 0.15 mmm = 3
θ3 = °
6.Hard
f1​ = 10 cmf2​ = 10 cm12 cm15 cm

Two thin lenses share an axis, 15 cm apart: lens 1 with f₁ = 10 cm and lens 2 with f₂ = 10 cm. An object stands 12 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 = 10 cms = 15 cmdo = 12 cm
di2 = cm

Answer key

  1. 1. β = 84.77 dB
  2. 2. f = 2 kHz
  3. 3. f5 = 535.9 Hz
  4. 4. L = 0.4985 m
  5. 5. θ3 = 0.7254 °
  6. 6. di2 = 8.182 cm

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