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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Name: ____________________   Date: ____________

1.Easy
L = 0.8 m

A string of length 0.8 m and mass 6 g carries transverse waves at 81.65 m/s. Find the tension T in the string.

L = 0.8 mm = 6 gv = 81.65 m/s
T = N
2.Easy
v = ?

Find the speed v of light in crown glass, which has a refractive index of 1.50.

n = 1.50c = 3.00 × 10⁸ m/s
v = m/s
3.Medium
FFdo​ = 20 cmf = 10 cm

An object stands 20 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 = 20 cmf = 10 cm
m =
4.Medium
S20 m/sO10 m/sf = 1000 Hz

A source of 1000 Hz moving at 20 m/s and an observer moving at 10 m/s move away from each other. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 1000 Hzv = 343 m/svs = 20 m/svo = 10 m/s
f′ = Hz
5.Hard
SO10 m/sf = 40 kHz

A parking sensor at rest sends ultrasound of 40 kHz towards a car that moves away at 10 m/s. Find the frequency f″ of the echo received back at the sensor (speed of sound 343 m/s).

f = 40 kHzu = 10 m/sv = 343 m/s
f″ = Hz
6.Hard
θa​ = ?n1​ = 1.55n2​ = 1.54n0​ = 1.00

An optical fibre has a core with n₁ = 1.55 and a cladding with n₂ = 1.54. 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 = 1.55n2 = 1.54n0 = 1.00
θa = °

Answer key

  1. 1. T = 50 N
  2. 2. v = 2 × 10⁸ m/s
  3. 3. m = −1
  4. 4. f′ = 917.4 Hz
  5. 5. f″ = 37734 Hz
  6. 6. θa = 10.12 °

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