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 = ?v = 1.2 m/sf = 2 Hz

A water wave has a frequency of 2 Hz and travels at 1.2 m/s. Find its wavelength λ.

f = 2 Hzv = 1.2 m/s
λ = m
2.Easy
λ = 0.148 mv = 1480 m/sf = ?

A sound wave in water travels at 1480 m/s with a wavelength of 0.148 m. Find its frequency f.

λ = 0.148 mv = 1480 m/s
f = kHz
3.Medium
S34 m/sOf = 600 Hz

A source of 600 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 = 600 Hzv = 343 m/svs = 34 m/s
f′ = Hz
4.Medium
P10 × 85 dB

One machine gives a sound level of 85 dB at a certain point. Find the level β at that point when 10 identical machines run at the same time (incoherent sources).

β1 = 85 dBn = 10
β = dB
5.Hard
SO30 m/sf = 35 kHz

A sensor at rest sends ultrasound of 35 kHz towards a car that approaches at 30 m/s and mixes the echo with the emitted signal. Find the beat frequency fb (speed of sound 343 m/s).

f = 35 kHzu = 30 m/sv = 343 m/s
fb = Hz
6.Hard
θa​ = ?n1​ = 1.52n2​ = 1.49n0​ = 1.00

An optical fibre has a core with n₁ = 1.52 and a cladding with n₂ = 1.49. 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 = 1.52n2 = 1.49n0 = 1.00
θa = °

Answer key

  1. 1. λ = 0.6 m
  2. 2. f = 10 kHz
  3. 3. f′ = 545.9 Hz
  4. 4. β = 95 dB
  5. 5. fb = 6709 Hz
  6. 6. θa = 17.49 °

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