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 = 0.8 m

A string of length 0.8 m and mass 8 g is stretched with a tension of 50 N. Find the speed v of transverse waves on it.

L = 0.8 mm = 8 gT = 50 N
v = m/s
2.Easy
60°θ₂ = ?ethanol, n1​ = 1.36diamond, n2​ = 2.42

A light ray in ethanol (n = 1.36) strikes a flat boundary with diamond (n = 2.42) at 60° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.36n2 = 2.42θ1 = 60°
θ2 = °
3.Medium
S15 m/sOf = 440 Hz

A source of 440 Hz moves at 15 m/s towards a stationary observer. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 440 Hzv = 343 m/svs = 15 m/s
f′ = Hz
4.Medium
L = ?n = 3

A string fixed at both ends must have its harmonic number 3 at 277 Hz; waves travel on it at 120 m/s. Find its length L.

v = 120 m/sn = 3f3 = 277 Hz
L = m
5.Hard
λ = 600 nmθ

A diffraction grating has 400 lines per millimetre. Light of wavelength 600 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 400 mm⁻¹λ = 600 nm
mmax =
6.Hard
λ = 589 nmθ

A diffraction grating has 400 lines per millimetre. Light of wavelength 589 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 400 mm⁻¹λ = 589 nm
mmax =

Answer key

  1. 1. v = 70.71 m/s
  2. 2. θ2 = 29.12 °
  3. 3. f′ = 460.1 Hz
  4. 4. L = 0.6498 m
  5. 5. mmax = 4
  6. 6. mmax = 4

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