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
λ = 2.5 mv = ?f = 0.8 Hz

A water wave has a frequency of 0.8 Hz and a wavelength of 2.5 m. Find its speed v.

f = 0.8 Hzλ = 2.5 m
v = m/s
2.Easy
L = 1.5 m

A string of length 1.5 m and mass 10 g carries transverse waves at 86.6 m/s. Find the tension T in the string.

L = 1.5 mm = 10 gv = 86.6 m/s
T = N
3.Medium
L = 0.75 mn = 5

A pipe closed at one end is 0.75 m long. The speed of sound is 343 m/s. Find the frequency f5 of its harmonic number 5.

v = 343 m/sn = 5L = 0.75 m
f5 = Hz
4.Medium
S34 m/sOf = 440 Hz

A source of 440 Hz moves at 34 m/s away from 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 = 34 m/s
f′ = Hz
5.Hard
θa​ = ?n1​ = 1.62n2​ = 1.57n0​ = 1.00

An optical fibre has a core with n₁ = 1.62 and a cladding with n₂ = 1.57. Find the largest angle θa to the fibre axis at which light from air can enter the end of the fibre and still be guided by total internal reflection.

n1 = 1.62n2 = 1.57n0 = 1.00
θa = °
6.Hard
λ = 450 nmθ3​ = ?

Light of wavelength 450 nm falls at right angles on a grating with 100 lines per millimetre. Find the angle θ3 of the order-3 maximum.

N = 100 mm⁻¹λ = 450 nmm = 3
θ3 = °

Answer key

  1. 1. v = 2 m/s
  2. 2. T = 50 N
  3. 3. f5 = 571.7 Hz
  4. 4. f′ = 400.3 Hz
  5. 5. θa = 23.54 °
  6. 6. θ3 = 7.759 °

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