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
20°θ₂ = ?air, n1​ = 1.00ethanol, n2​ = 1.36

A light ray in air (n = 1.00) strikes a flat boundary with ethanol (n = 1.36) at 20° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.00n2 = 1.36θ1 = 20°
θ2 = °
2.Easy
λ = ?v = 340 m/sf = 50 Hz

A sound wave in air has a frequency of 50 Hz and travels at 340 m/s. Find its wavelength λ.

f = 50 Hzv = 340 m/s
λ = m
3.Medium
L = 0.8 mn = 4

A string fixed at both ends is 0.8 m long; waves travel on it at 240 m/s. Find the frequency f4 of its harmonic number 4.

v = 240 m/sn = 4L = 0.8 m
f4 = Hz
4.Medium
θc = ?90°diamond, n1​ = 2.42ethanol, n2​ = 1.36

Light travels in diamond (n = 2.42) towards a flat boundary with ethanol (n = 1.36). Find the critical angle θc beyond which it is totally reflected.

n1 = 2.42n2 = 1.36
θc = °
5.Hard
SO10 m/sf = 40 kHz

A sensor at rest sends ultrasound of 40 kHz towards a car that approaches at 10 m/s and mixes the echo with the emitted signal. Find the beat frequency fb (speed of sound 343 m/s).

f = 40 kHzu = 10 m/sv = 343 m/s
fb = Hz
6.Hard
θn1​ = 1.48n2​ = 1.45n0​ = 1.00

An optical fibre has a core with n₁ = 1.48 and a cladding with n₂ = 1.45. Find its numerical aperture NA.

n1 = 1.48n2 = 1.45
NA =

Answer key

  1. 1. θ2 = 14.57 °
  2. 2. λ = 6.8 m
  3. 3. f4 = 600 Hz
  4. 4. θc = 34.19 °
  5. 5. fb = 2402 Hz
  6. 6. NA = 0.2965

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