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 = 3 × 10⁻⁶ W/m²

The sound intensity near a classroom is 3 × 10⁻⁶ W/m². Find the sound intensity level β in decibels.

I = 3 × 10⁻⁶ W/m²I0 = 10⁻¹² W/m²
β = dB
2.Easy
λ = 3.43 mv = 343 m/sf = ?

A sound wave in air travels at 343 m/s with a wavelength of 3.43 m. Find its frequency f.

λ = 3.43 mv = 343 m/s
f = Hz
3.Medium
L = ?n = 3

A pipe closed at one end must have its harmonic number 3 at 429 Hz. The speed of sound is 343 m/s. Find the length L of the pipe.

v = 343 m/sn = 3f3 = 429 Hz
L = m
4.Medium
θc = ?90°glycerol, n1​ = 1.47ethanol, n2​ = 1.36

Light travels in glycerol (n = 1.47) towards a flat boundary with ethanol (n = 1.36). Find the critical angle θc beyond which it is totally reflected.

n1 = 1.47n2 = 1.36
θc = °
5.Hard
SO20 m/sf = 20 kHz

A sensor at rest sends ultrasound of 20 kHz towards a car that moves away at 20 m/s and mixes the echo with the emitted signal. Find the beat frequency fb (speed of sound 343 m/s).

f = 20 kHzu = 20 m/sv = 343 m/s
fb = Hz
6.Hard
λ = 656 nmθ

A diffraction grating has 1200 lines per millimetre. Light of wavelength 656 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 1200 mm⁻¹λ = 656 nm
mmax =

Answer key

  1. 1. β = 64.77 dB
  2. 2. f = 100 Hz
  3. 3. L = 0.5997 m
  4. 4. θc = 67.69 °
  5. 5. fb = 2204 Hz
  6. 6. mmax = 1

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