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
Pβ = 85 dB

The sound intensity level at a point is 85 dB. Find the sound intensity I.

β = 85 dBI0 = 10⁻¹² W/m²
I = µW/m²
2.Easy
Pβ = 60 dB

The sound intensity level at a point is 60 dB. Find the sound intensity I.

β = 60 dBI0 = 10⁻¹² W/m²
I = µW/m²
3.Medium
100 dB?2 m8 m

A small source sends sound equally in all directions. The level is 100 dB at 2 m from it. Find the level β2 at 8 m, ignoring absorption and reflections.

β1 = 100 dBr1 = 2 mr2 = 8 m
β2 = dB
4.Medium
42°90°n1​ = ?air, n2​ = 1.00

Light inside a transparent block is totally reflected at the boundary with air (n = 1.00) for every angle of incidence above 42°. Find the refractive index n1 of the block.

θc = 42°n2 = 1.00
n1 =
5.Hard
SO15 m/sf = 40 kHz

A sensor at rest sends ultrasound of 40 kHz towards a car that approaches at 15 m/s and mixes the echo with the emitted signal. Find the beat frequency fb (speed of sound 343 m/s).

f = 40 kHzu = 15 m/sv = 343 m/s
fb = Hz
6.Hard
λ = 486 nmθ1​ = ?

Light of wavelength 486 nm falls at right angles on a grating with 300 lines per millimetre. Find the angle θ1 of the order-1 maximum.

N = 300 mm⁻¹λ = 486 nmm = 1
θ1 = °

Answer key

  1. 1. I = 316.2 µW/m²
  2. 2. I = 1 µW/m²
  3. 3. β2 = 87.96 dB
  4. 4. n1 = 1.494
  5. 5. fb = 3659 Hz
  6. 6. θ1 = 8.384 °

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