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
60°θ₂ = ?glycerol, n1​ = 1.47acrylic, n2​ = 1.49

A light ray in glycerol (n = 1.47) strikes a flat boundary with acrylic (n = 1.49) at 60° to the normal. Find the angle of refraction θ2, measured from the normal.

n1 = 1.47n2 = 1.49θ1 = 60°
θ2 = °
2.Easy
v = ?

Find the speed v of light in diamond, which has a refractive index of 2.42.

n = 2.42c = 3.00 × 10⁸ m/s
v = m/s
3.Medium
FFdo​ = 30 cmf = 10 cm

An object stands 30 cm in front of a thin converging lens with a focal length of 10 cm. Find the magnification m (negative for an inverted image).

do = 30 cmf = 10 cm
m =
4.Medium
L = 0.4 mn = 2

A pipe open at both ends is 0.4 m long. The speed of sound is 343 m/s. Find the frequency f2 of its harmonic number 2.

v = 343 m/sn = 2L = 0.4 m
f2 = Hz
5.Hard
SO5 m/sf = 35 kHz

A parking sensor at rest sends ultrasound of 35 kHz towards a car that approaches at 5 m/s. Find the frequency f″ of the echo received back at the sensor (speed of sound 343 m/s).

f = 35 kHzu = 5 m/sv = 343 m/s
f″ = Hz
6.Hard
Fdo​ = 12 cmR = 40 cm

An object is 12 cm in front of a concave mirror with a radius of curvature of 40 cm. Find the image distance di, positive for an image in front of the mirror (real) and negative for one behind it (virtual).

do = 12 cmR = 40 cm
di = cm

Answer key

  1. 1. θ2 = 58.69 °
  2. 2. v = 1.24 × 10⁸ m/s
  3. 3. m = −0.5
  4. 4. f2 = 857.5 Hz
  5. 5. f″ = 36036 Hz
  6. 6. di = −30 cm

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