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 = 0.5 m

A string of length 0.5 m and mass 15 g is stretched with a tension of 150 N. Find the speed v of transverse waves on it.

L = 0.5 mm = 15 gT = 150 N
v = m/s
2.Easy
L = 0.8 m

A string of length 0.8 m and mass 5 g carries transverse waves at 138.6 m/s. Find the tension T in the string.

L = 0.8 mm = 5 gv = 138.6 m/s
T = N
3.Medium
L = ?n = 5

A string fixed at both ends must have its harmonic number 5 at 450 Hz; waves travel on it at 180 m/s. Find its length L.

v = 180 m/sn = 5f5 = 450 Hz
L = m
4.Medium
90 dB?10 m30 m

A small source sends sound equally in all directions. The level is 90 dB at 10 m from it. Find the level β2 at 30 m, ignoring absorption and reflections.

β1 = 90 dBr1 = 10 mr2 = 30 m
β2 = dB
5.Hard
SO25 m/sf = 25 kHz

A parking sensor at rest sends ultrasound of 25 kHz towards a car that approaches at 25 m/s. Find the frequency f″ of the echo received back at the sensor (speed of sound 343 m/s).

f = 25 kHzu = 25 m/sv = 343 m/s
f″ = Hz
6.Hard
f1​ = 5 cmf2​ = 20 cm50 cm60 cm

Two thin lenses share an axis, 60 cm apart: lens 1 with f₁ = 5 cm and lens 2 with f₂ = 20 cm. An object stands 50 cm in front of lens 1. Find the position di2 of the final image measured from lens 2 (positive beyond lens 2, real-is-positive convention).

f1 = 5 cmf2 = 20 cms = 60 cmdo = 50 cm
di2 = cm

Answer key

  1. 1. v = 70.71 m/s
  2. 2. T = 120.1 N
  3. 3. L = 1 m
  4. 4. β2 = 80.46 dB
  5. 5. f″ = 28931 Hz
  6. 6. di2 = 31.61 cm

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