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 = 1.2 m

A string of length 1.2 m and mass 20 g is stretched with a tension of 200 N. Find the speed v of transverse waves on it.

L = 1.2 mm = 20 gT = 200 N
v = m/s
2.Easy
λ = ?v = 3.00 × 10⁸ m/sf = 100 MHz

A radio wave has a frequency of 100 MHz and travels at 3.00 × 10⁸ m/s. Find its wavelength λ.

f = 100 MHzv = 3.00 × 10⁸ m/s
λ = m
3.Medium
L = 0.5 mn = 5

A string fixed at both ends is 0.5 m long; waves travel on it at 180 m/s. Find the frequency f5 of its harmonic number 5.

v = 180 m/sn = 5L = 0.5 m
f5 = Hz
4.Medium
L = ?n = 7

A pipe closed at one end must have its harmonic number 7 at 400 Hz. The speed of sound is 343 m/s. Find the length L of the pipe.

v = 343 m/sn = 7f7 = 400 Hz
L = m
5.Hard
θn1​ = 1.62n2​ = 1.52n0​ = 1.00

An optical fibre has a core with n₁ = 1.62 and a cladding with n₂ = 1.52. Find its numerical aperture NA.

n1 = 1.62n2 = 1.52
NA =
6.Hard
θn1​ = 1.48n2​ = 1.38n0​ = 1.00

An optical fibre has a core with n₁ = 1.48 and a cladding with n₂ = 1.38. Find its numerical aperture NA.

n1 = 1.48n2 = 1.38
NA =

Answer key

  1. 1. v = 109.5 m/s
  2. 2. λ = 3 m
  3. 3. f5 = 900 Hz
  4. 4. L = 1.501 m
  5. 5. NA = 0.5604
  6. 6. NA = 0.5348

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