Waves, Sound & Light — Science

  1. Grade 8 — Wave Properties
  2. Grade 8 — Sound Waves
  3. Grade 8 — Light & the Electromagnetic Spectrum
  4. Grade 12 — Wave Properties
  5. Grade 12 — Sound
  6. Grade 12 — Light & the Electromagnetic Spectrum
  7. Grade 12 — Reflection, Refraction & Optics

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Problem 1

A sound wave travels through air at 340 m/s with a frequency of 170 Hz. What is its wavelength? Use v = fλ.
Hints

Rearrange v = fλ to solve for the wavelength λ.

λ = v ÷ f.

λ = 340 ÷ 170.

Answer and explanation

2 m

From v = fλ, the wavelength is λ = v ÷ f.

λ = 340 ÷ 170.

λ = 2 m.

Problem 2

A radio station broadcasts at a frequency of 90 MHz (90 × 10^6 Hz). Radio waves travel at the speed of light, 3 × 10^8 m/s. What is the wavelength of the signal? Use v = fλ.
Hints

Radio waves are electromagnetic, so they travel at c = 3 × 10^8 m/s.

λ = c ÷ f.

λ = (3 × 10^8) ÷ (90 × 10^6).

Answer and explanation

3.33 m

Wavelength λ = c ÷ f = (3 × 10^8) ÷ (90 × 10^6).

= (3 × 10^8) ÷ (9 × 10^7) = 30 ÷ 9.

λ ≈ 3.33 m.

Problem 3

A wave on a rope has a period of 0.25 s and a wavelength of 3 m. What is the wave's speed? First find the frequency from the period, then use v = fλ.
Hints

Frequency is the reciprocal of the period: f = 1 ÷ T.

f = 1 ÷ 0.25 = 4 Hz.

Then v = fλ = 4 · 3.

Answer and explanation

12 m/s

Frequency f = 1 ÷ T = 1 ÷ 0.25 = 4 Hz.

Wave speed v = fλ = 4 · 3.

v = 12 m/s.

Problem 4

A hiker shouts toward a cliff and hears the echo 2.0 s later. If sound travels at 343 m/s, how far away is the cliff? Remember the sound must travel to the cliff and back.
Hints

In 2.0 s the sound makes a round trip — out to the cliff and back.

Total distance traveled = speed × time = 343 · 2.0 = 686 m.

The cliff is only half of that round-trip distance.

Answer and explanation

343 m

Total path of the sound = 343 · 2.0 = 686 m (there and back).

The cliff distance is half the round trip: 686 ÷ 2.

Distance = 343 m.

Problem 5

Which list places these electromagnetic waves in order of INCREASING frequency (lowest first)?
  1. Radio waves, infrared, visible light, X-rays
  2. X-rays, visible light, infrared, radio waves
  3. Visible light, radio waves, infrared, X-rays
  4. Infrared, radio waves, X-rays, visible light
Hints

Across the EM spectrum, frequency rises as wavelength shrinks.

Radio waves have the lowest frequency; gamma and X-rays the highest.

Order of increasing frequency: radio → microwave → infrared → visible → ultraviolet → X-ray → gamma.

Answer and explanation

Radio waves, infrared, visible light, X-rays

Frequency increases from radio waves up through infrared, then visible light, then X-rays.

Only one option follows that low-to-high order the whole way.

Radio, infrared, visible, X-rays is increasing frequency, so A is correct.

Problem 6

A microwave oven produces electromagnetic waves with a wavelength of 0.12 m. Using the speed of light c = 3 × 10^8 m/s, what is their frequency in GHz? (1 GHz = 10^9 Hz.)
Hints

Rearrange c = fλ to f = c ÷ λ.

f = (3 × 10^8) ÷ 0.12 = 2.5 × 10^9 Hz.

Convert to GHz by dividing by 10^9.

Answer and explanation

2.5 GHz

f = c ÷ λ = (3 × 10^8) ÷ 0.12 = 2.5 × 10^9 Hz.

Since 1 GHz = 10^9 Hz, divide by 10^9.

f = 2.5 GHz.

Problem 7

A wave travels 60 m in 4 s. If its wavelength is 5 m, what is its frequency? First find the wave's speed, then use v = fλ.
Hints

Speed = distance ÷ time.

v = 60 ÷ 4 = 15 m/s.

Then f = v ÷ λ = 15 ÷ 5.

Answer and explanation

3 Hz

Wave speed v = distance ÷ time = 60 ÷ 4 = 15 m/s.

From v = fλ, frequency f = v ÷ λ = 15 ÷ 5.

f = 3 Hz.

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