Wavelength, frequency and speed
A sound wave, drawn on a graph, has crests, the high points. How far apart are they?
The graph shows how crowded the air is. A crest is a high point of this graph. So a crest marks the most crowded place.
- A sound wave in air. It shakes 170 times a second.
- The gap from crest to crest is its wavelength. Here it is 2 m.
- A wave that shakes 340 times a second has its crests closer. The gap is 1 m.
The answer is the wavelength. In the first wave, it is 2 m.
Rule
The wavelength is the distance between neighbouring crests, or neighbouring troughs. Neighbouring crests are two crests next to each other. The symbol for wavelength is λ. Its unit is the metre. A trough is a low point of the graph. So a trough marks the least crowded place.
Call the time period T. In time T, the wave moves forward by one wavelength. So speed = distance ÷ time = λ ÷ T. Now λ ÷ T = λ × (1 ÷ T). Since 1 ÷ T is the frequency ν, this gives:
Rule: Speed = wavelength × frequency, or v = λ × ν.
Here v is speed, λ is wavelength, ν (nu) is frequency.
In one medium at one temperature, the speed does not change. So a higher frequency gives a shorter wavelength. Doubling the frequency halves the wavelength.
| Frequency | Wavelength | Speed |
|---|---|---|
| 170 Hz | 340 ÷ 170 = 2 m | 2 × 170 = 340 |
| 340 Hz | 340 ÷ 340 = 1 m | 1 × 340 = 340 |
| 680 Hz | 340 ÷ 680 = 0.5 m | 0.5 × 680 = 340 |
The speed depends on the medium. A 500 Hz source gives these wavelengths:
- In air at 340 m/s: 340 ÷ 500 = 0.68 m.
- In water at 1500 m/s: 1500 ÷ 500 = 3 m.
- In steel at 5000 m/s: 5000 ÷ 500 = 10 m.
A graph can show the wavelength. Suppose two neighbouring crests are 8 m apart. The speed is 340 m/s. From v = λ × ν, we get ν = v ÷ λ. Then the frequency is 340 ÷ 8 = 42.5 Hz.
Set the frequency and wavelength. Make the speed 340 m/s.
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