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 × 10⁻⁵ W/m²

The sound intensity near a vacuum cleaner is 3 × 10⁻⁵ W/m². Find the sound intensity level β in decibels.

I = 3 × 10⁻⁵ W/m²I0 = 10⁻¹² W/m²
β = dB
2.Easy
v = 2 × 10⁸ m/s

Light travels at 2 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 2 × 10⁸ m/sc = 3.00 × 10⁸ m/s
n =
3.Medium
L = 0.75 mn = 4

A string fixed at both ends is 0.75 m long; waves travel on it at 100 m/s. Find the frequency f4 of its harmonic number 4.

v = 100 m/sn = 4L = 0.75 m
f4 = Hz
4.Medium
S30 m/sO5 m/sf = 440 Hz

A source of 440 Hz moving at 30 m/s and an observer moving at 5 m/s approach each other. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 440 Hzv = 343 m/svs = 30 m/svo = 5 m/s
f′ = Hz
5.Hard
λ = 405 nmθ1​ = ?

Light of wavelength 405 nm falls at right angles on a grating with 200 lines per millimetre. Find the angle θ1 of the order-1 maximum.

N = 200 mm⁻¹λ = 405 nmm = 1
θ1 = °
6.Hard
f1​ = 5 cmf2​ = 15 cm15 cm10 cm

Two thin lenses share an axis, 10 cm apart: lens 1 with f₁ = 5 cm and lens 2 with f₂ = 15 cm. An object stands 15 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 = 5 cmf2 = 15 cms = 10 cmdo = 15 cm
di2 = cm

Answer key

  1. 1. β = 74.77 dB
  2. 2. n = 1.5
  3. 3. f4 = 266.7 Hz
  4. 4. f′ = 489.2 Hz
  5. 5. θ1 = 4.646 °
  6. 6. di2 = −3 cm

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