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 m

A string of length 1 m and mass 6 g is stretched with a tension of 250 N. Find the speed v of transverse waves on it.

L = 1 mm = 6 gT = 250 N
v = m/s
2.Easy
L = 1.2 m

A string of length 1.2 m and mass 6 g is stretched with a tension of 120 N. Find the speed v of transverse waves on it.

L = 1.2 mm = 6 gT = 120 N
v = m/s
3.Medium
42°90°n1​ = ?water, n2​ = 1.33

Light inside a transparent block is totally reflected at the boundary with water (n = 1.33) for every angle of incidence above 42°. Find the refractive index n1 of the block.

θc = 42°n2 = 1.33
n1 =
4.Medium
L = 0.5 mn = 3

A string fixed at both ends is 0.5 m long; waves travel on it at 200 m/s. Find the frequency f3 of its harmonic number 3.

v = 200 m/sn = 3L = 0.5 m
f3 = Hz
5.Hard
λ = 589 nmθ2​ = ?

Light of wavelength 589 nm falls at right angles on a grating with 100 lines per millimetre. Find the angle θ2 of the order-2 maximum.

N = 100 mm⁻¹λ = 589 nmm = 2
θ2 = °
6.Hard
λ = ?45°

A grating with 600 lines per millimetre shows the order-2 maximum of a spectral line at 45° from the straight-through direction. Find the wavelength λ of the line.

N = 600 mm⁻¹θ2 = 45°m = 2
λ = nm

Answer key

  1. 1. v = 204.1 m/s
  2. 2. v = 154.9 m/s
  3. 3. n1 = 1.988
  4. 4. f3 = 600 Hz
  5. 5. θ2 = 6.765 °
  6. 6. λ = 589.3 nm

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