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 = ?

Light with a wavelength of 589 nm in vacuum enters ethanol (n = 1.36). Find its wavelength λ inside the material.

n = 1.36λ0 = 589 nm
λ = nm
2.Easy
λ = 3.141 mv = 3.00 × 10⁸ m/sf = ?

A radio wave travels at 3.00 × 10⁸ m/s with a wavelength of 3.141 m. Find its frequency f.

λ = 3.141 mv = 3.00 × 10⁸ m/s
f = MHz
3.Medium
L = ?n = 2

A string fixed at both ends must have its harmonic number 2 at 308 Hz; waves travel on it at 200 m/s. Find its length L.

v = 200 m/sn = 2f2 = 308 Hz
L = m
4.Medium
FFdo​ = 25 cmf = −25 cm

An object stands 25 cm in front of a thin diverging lens with a focal length of 25 cm. Find the image distance di. Use the sign convention 1/f = 1/do + 1/di (f < 0 for a diverging lens, di < 0 for a virtual image).

do = 25 cmf = −25 cm
di = cm
5.Hard
λ = 486 nmθ1​ = ?

Light of wavelength 486 nm falls at right angles on a grating with 800 lines per millimetre. Find the angle θ1 of the order-1 maximum.

N = 800 mm⁻¹λ = 486 nmm = 1
θ1 = °
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. λ = 433.1 nm
  2. 2. f = 95.5 MHz
  3. 3. L = 0.6494 m
  4. 4. di = −12.5 cm
  5. 5. θ1 = 22.88 °
  6. 6. λ = 589.3 nm

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