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 × 10⁻⁸ W/m²

The sound intensity near a quiet library is 3 × 10⁻⁸ W/m². Find the sound intensity level β in decibels.

I = 3 × 10⁻⁸ W/m²I0 = 10⁻¹² W/m²
β = dB
2.Easy
L = 0.8 m

A string of length 0.8 m and mass 15 g carries transverse waves at 51.64 m/s. Find the tension T in the string.

L = 0.8 mm = 15 gv = 51.64 m/s
T = N
3.Medium
L = 1 mn = 5

A pipe open at both ends is 1 m long. The speed of sound is 343 m/s. Find the frequency f5 of its harmonic number 5.

v = 343 m/sn = 5L = 1 m
f5 = Hz
4.Medium
S30 m/sOf = 1000 Hz

A source of 1000 Hz moves at 30 m/s away from a stationary observer. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 1000 Hzv = 343 m/svs = 30 m/s
f′ = Hz
5.Hard
SO15 m/sf = 20 kHz

A sensor at rest sends ultrasound of 20 kHz towards a car that approaches at 15 m/s and mixes the echo with the emitted signal. Find the beat frequency fb (speed of sound 343 m/s).

f = 20 kHzu = 15 m/sv = 343 m/s
fb = Hz
6.Hard
θn1​ = 1.62n2​ = 1.6n0​ = 1.00

An optical fibre has a core with n₁ = 1.62 and a cladding with n₂ = 1.6. Find its numerical aperture NA.

n1 = 1.62n2 = 1.6
NA =

Answer key

  1. 1. β = 44.77 dB
  2. 2. T = 50 N
  3. 3. f5 = 857.5 Hz
  4. 4. f′ = 919.6 Hz
  5. 5. fb = 1829 Hz
  6. 6. NA = 0.2538

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