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

A string of length 1.2 m and mass 20 g is stretched with a tension of 150 N. Find the speed v of transverse waves on it.

L = 1.2 mm = 20 gT = 150 N

v = m/s

2.Easy

A light ray in acrylic (n = 1.49) strikes a flat boundary with diamond (n = 2.42) at 45° to the normal. Find the angle of refraction θ₂, measured from the normal.

n₁ = 1.49n₂ = 2.42θ₁ = 45°

θ₂ = °

3.Medium

A source of 300 Hz moves at 20 m/s away from a stationary observer. The speed of sound is 343 m/s. Find the frequency f′ that the observer hears.

f = 300 Hzv = 343 m/sv_s = 20 m/s

f′ = Hz

4.Medium

An object 3 cm tall stands 20 cm in front of a thin diverging lens with a focal length of 5 cm. Find the image height h_i (negative for an inverted image).

h_o = 3 cmd_o = 20 cmf = −5 cm

h_i = cm

5.Hard

A grating with 300 lines per millimetre shows the order-1 maximum of a spectral line at 9.5° from the straight-through direction. Find the wavelength λ of the line.

N = 300 mm⁻¹θ₁ = 9.5°m = 1

λ = nm

6.Hard

An optical fibre has a core with n₁ = 1.62 and a cladding with n₂ = 1.6. Find the largest angle θ_a 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 = 1.6n₀ = 1.00

θ_a = °

Answer key

1. v = 94.87 m/s
2. θ₂ = 25.81 °
3. f′ = 283.5 Hz
4. h_i = 0.6 cm
5. λ = 550.2 nm
6. θ_a = 14.7 °

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