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
L = 1.5 m

A string of length 1.5 m and mass 4 g is stretched with a tension of 60 N. Find the speed v of transverse waves on it.

L = 1.5 mm = 4 gT = 60 N
v = m/s
2.Easy
PI = 3 × 10⁻² W/m²

The sound intensity near a rock concert is 3 × 10⁻² W/m². Find the sound intensity level β in decibels.

I = 3 × 10⁻² W/m²I0 = 10⁻¹² W/m²
β = dB
3.Medium
L = 0.65 mn = 3

A pipe closed at one end is 0.65 m long. The speed of sound is 343 m/s. Find the frequency f3 of its harmonic number 3.

v = 343 m/sn = 3L = 0.65 m
f3 = Hz
4.Medium
L = ?n = 1

A string fixed at both ends must have its fundamental (first harmonic) at 75 Hz; waves travel on it at 120 m/s. Find its length L.

v = 120 m/sn = 1f1 = 75 Hz
L = m
5.Hard
f1​ = 20 cmf2​ = 15 cm50 cm60 cm

Two thin lenses share an axis, 60 cm apart: lens 1 with f₁ = 20 cm and lens 2 with f₂ = 15 cm. An object stands 50 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 = 20 cmf2 = 15 cms = 60 cmdo = 50 cm
di2 = cm
6.Hard
λ = 550 nma = 0.12 mmL = 3 m

Light of wavelength 550 nm passes through a single slit 0.12 mm wide. Find the width w of the central bright maximum on a screen 3 m away (between the first dark fringes on either side).

λ = 550 nma = 0.12 mmL = 3 m
w = mm

Answer key

  1. 1. v = 150 m/s
  2. 2. β = 104.8 dB
  3. 3. f3 = 395.8 Hz
  4. 4. L = 0.8 m
  5. 5. di2 = 34.29 cm
  6. 6. w = 27.5 mm

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