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 = 2 m

A string of length 2 m and mass 15 g carries transverse waves at 81.65 m/s. Find the tension T in the string.

L = 2 mm = 15 gv = 81.65 m/s
T = N
2.Easy
v = 2.01 × 10⁸ m/s

Light travels at 2.01 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 2.01 × 10⁸ m/sc = 3.00 × 10⁸ m/s
n =
3.Medium
L = 0.75 mn = 3

A string fixed at both ends is 0.75 m long; waves travel on it at 150 m/s. Find the frequency f3 of its harmonic number 3.

v = 150 m/sn = 3L = 0.75 m
f3 = Hz
4.Medium
L = ?n = 3

A pipe open at both ends must have its harmonic number 3 at 1286 Hz. The speed of sound is 343 m/s. Find the length L of the pipe.

v = 343 m/sn = 3f3 = 1286 Hz
L = m
5.Hard
SO25 m/sf = 25 kHz

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

f = 25 kHzu = 25 m/sv = 343 m/s
fb = Hz
6.Hard
λ = 650 nma = 0.12 mm

Light of wavelength 650 nm passes through a single slit 0.12 mm wide. Find the angle θ3 of dark fringe number 3 from the straight-through direction.

λ = 650 nma = 0.12 mmm = 3
θ3 = °

Answer key

  1. 1. T = 50 N
  2. 2. n = 1.493
  3. 3. f3 = 300 Hz
  4. 4. L = 0.4001 m
  5. 5. fb = 3931 Hz
  6. 6. θ3 = 0.9311 °

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