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
λ = 29.6 mv = ?f = 50 Hz

A sound wave in water has a frequency of 50 Hz and a wavelength of 29.6 m. Find its speed v.

f = 50 Hzλ = 29.6 m
v = m/s
2.Easy
L = 2.5 m

A string of length 2.5 m and mass 10 g is stretched with a tension of 80 N. Find the speed v of transverse waves on it.

L = 2.5 mm = 10 gT = 80 N
v = m/s
3.Medium
90 dB?10 m30 m

A small source sends sound equally in all directions. The level is 90 dB at 10 m from it. Find the level β2 at 30 m, ignoring absorption and reflections.

β1 = 90 dBr1 = 10 mr2 = 30 m
β2 = dB
4.Medium
38°90°n1​ = ?crown glass, n2​ = 1.50

Light inside a transparent block is totally reflected at the boundary with crown glass (n = 1.50) for every angle of incidence above 38°. Find the refractive index n1 of the block.

θc = 38°n2 = 1.50
n1 =
5.Hard
θa​ = ?n1​ = 1.46n2​ = 1.38n0​ = 1.00

An optical fibre has a core with n₁ = 1.46 and a cladding with n₂ = 1.38. Find the largest angle θa to the fibre axis at which light from air can enter the end of the fibre and still be guided by total internal reflection.

n1 = 1.46n2 = 1.38n0 = 1.00
θa = °
6.Hard
λ = 656 nmθ1​ = ?

Light of wavelength 656 nm falls at right angles on a grating with 600 lines per millimetre. Find the angle θ1 of the order-1 maximum.

N = 600 mm⁻¹λ = 656 nmm = 1
θ1 = °

Answer key

  1. 1. v = 1480 m/s
  2. 2. v = 141.4 m/s
  3. 3. β2 = 80.46 dB
  4. 4. n1 = 2.436
  5. 5. θa = 28.47 °
  6. 6. θ1 = 23.18 °

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