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
PI = 2.5 × 10⁻⁵ W/m²

The sound intensity near a vacuum cleaner is 2.5 × 10⁻⁵ W/m². Find the sound intensity level β in decibels.

I = 2.5 × 10⁻⁵ W/m²I0 = 10⁻¹² W/m²
β = dB
2.Easy
35°θ₂ = ?air, n1​ = 1.00glycerol, n2​ = 1.47

A light ray in air (n = 1.00) strikes a flat boundary with glycerol (n = 1.47) at 35° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.00n2 = 1.47θ1 = 35°
θ2 = °
3.Medium
θc = ?90°glycerol, n1​ = 1.47air, n2​ = 1.00

Light travels in glycerol (n = 1.47) towards a flat boundary with air (n = 1.00). Find the critical angle θc beyond which it is totally reflected.

n1 = 1.47n2 = 1.00
θc = °
4.Medium
P5 × 65 dB

One machine gives a sound level of 65 dB at a certain point. Find the level β at that point when 5 identical machines run at the same time (incoherent sources).

β1 = 65 dBn = 5
β = dB
5.Hard
λ = 589 nmθ1​ = ?

Light of wavelength 589 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 = 589 nmm = 1
θ1 = °
6.Hard
SO5 m/sf = 25 kHz

A sensor at rest sends ultrasound of 25 kHz towards a car that approaches at 5 m/s and mixes the echo with the emitted signal. Find the beat frequency fb (speed of sound 343 m/s).

f = 25 kHzu = 5 m/sv = 343 m/s
fb = Hz

Answer key

  1. 1. β = 73.98 dB
  2. 2. θ2 = 22.97 °
  3. 3. θc = 42.86 °
  4. 4. β = 71.99 dB
  5. 5. θ1 = 28.11 °
  6. 6. fb = 739.6 Hz

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