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Frequency and wavelength

Waves, sound and light · level 5, lesson 2 of 6

A question to start

An orchestra tunes to a note of 440 Hz. In Mars air, sound is slower. Would the waves of that note be longer or shorter on Mars?

The idea

In one second, \(f\) waves pass a point, each of length \(\lambda\). So the wave travels \(f\lambda\) metres each second. This is the wave equation:

\[v = f\lambda.\]

The frequency is set by the source. The speed is set by the medium. So when the same note moves into a slower medium, its wavelength gets shorter.

A 440 Hz note Mars air Earth air
Speed of sound about 240 m/s about 340 m/s
Wavelength 0.55 m 0.77 m
Earth: λ = 0.77 mMars: λ = 0.55 m, same frequency

Worked examples

1. Earth. \(\lambda = v/f = 340/440 = 0.77\) m.

2. Mars. \(\lambda = 240/440 = 0.55\) m.

3. Ingenuity's hum. At 84 Hz in Mars air: \(\lambda = 240/84 = 2.9\) m.

Try it

  1. Write the wave equation and say what each letter means.
  2. A wave on a rope has a frequency of 4 Hz and a wavelength of 0.5 m. Find its speed.
  3. Find the wavelength of a 20 Hz sound in Earth air.
  4. A sound goes from air into water, where it is about 4.4 times faster. What happens to its frequency and wavelength?
Answers
  1. \(v = f\lambda\): speed = frequency × wavelength.
  2. \(4 \times 0.5 = 2\) m/s.
  3. \(340/20 = 17\) m.
  4. The frequency stays the same; the wavelength becomes about 4.4 times longer.

Common mistake

"A higher frequency makes the wave go faster." In one medium, all frequencies travel at about the same speed. A higher frequency gives a shorter wavelength, not a faster wave.

Where it leads