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
v = 1.24 × 10⁸ m/s

Light travels at 1.24 × 10⁸ m/s in a transparent material. Find its refractive index n.

v = 1.24 × 10⁸ m/sc = 3.00 × 10⁸ m/s
n =
2.Easy
λ = ?

Light with a wavelength of 450 nm in vacuum enters acrylic (n = 1.49). Find its wavelength λ inside the material.

n = 1.49λ0 = 450 nm
λ = nm
3.Medium
θc = ?90°diamond, n1​ = 2.42flint glass, n2​ = 1.62

Light travels in diamond (n = 2.42) towards a flat boundary with flint glass (n = 1.62). Find the critical angle θc beyond which it is totally reflected.

n1 = 2.42n2 = 1.62
θc = °
4.Medium
L = 0.65 mn = 5

A string fixed at both ends is 0.65 m long; waves travel on it at 120 m/s. Find the frequency f5 of its harmonic number 5.

v = 120 m/sn = 5L = 0.65 m
f5 = Hz
5.Hard
SO20 m/sf = 35 kHz

A parking sensor at rest sends ultrasound of 35 kHz towards a car that approaches at 20 m/s. Find the frequency f″ of the echo received back at the sensor (speed of sound 343 m/s).

f = 35 kHzu = 20 m/sv = 343 m/s
f″ = Hz
6.Hard
λ = 405 nmθ

A diffraction grating has 400 lines per millimetre. Light of wavelength 405 nm falls on it at right angles. What is the highest order mmax of bright maximum that can be seen?

N = 400 mm⁻¹λ = 405 nm
mmax =

Answer key

  1. 1. n = 2.419
  2. 2. λ = 302 nm
  3. 3. θc = 42.02 °
  4. 4. f5 = 461.5 Hz
  5. 5. f″ = 39334 Hz
  6. 6. mmax = 6

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