How Long Is a 7870 Hz Wavelength?
A 7870 Hz sound wave has a wavelength of 0.04 meters, 4.36 cm, 0.14 feet (0 feet and 1.72 inches) or 1.72 inches when traveling in air at 20°C (68°F).
The formula for the wavelenght is λ = c/f where:
cis the celerity (speed) of sound = 343.21 m/s or 1126.03 ft/s in air at 20°C (68°F).fis the frequency = 7870 Hz
λ of 0.04 meters, or 0.14 feet.
7870 Hz Wavelength Depending on Temperature
The speed of sound in air depends on temperature. Here is how the wavelenght of a 7870 Hz sound wave will vary according to temperature:
| Temp (°C) | Temp (°F) | 7870 Hz wavelength (cm) | 7870 Hz wavelength (in) |
|---|---|---|---|
| -40 | -40 | 3.8892 | 1.5312 |
| -35 | -31 | 3.9307 | 1.5475 |
| -30 | -22 | 3.9718 | 1.5637 |
| -25 | -13 | 4.0124 | 1.5797 |
| -20 | -4 | 4.0526 | 1.5955 |
| -15 | 5 | 4.0924 | 1.6112 |
| -10 | 14 | 4.1319 | 1.6267 |
| -5 | 23 | 4.1710 | 1.6421 |
| 0 | 32 | 4.2097 | 1.6573 |
| 5 | 41 | 4.2480 | 1.6724 |
| 10 | 50 | 4.2860 | 1.6874 |
| 15 | 59 | 4.3237 | 1.7022 |
| 20 | 68 | 4.3610 | 1.7169 |
| 25 | 77 | 4.3981 | 1.7315 |
| 30 | 86 | 4.4348 | 1.7460 |
| 35 | 95 | 4.4712 | 1.7603 |
| 40 | 104 | 4.5074 | 1.7746 |
7870 Hz Half Wavelength and Standing Waves
The half wavelength of a 7870 Hz sound wave is 0.02 meters, 2.18 cm, 0.07 feet (0 feet and 0.86 inches) or 0.86 inches when travelling in air at 20°C (68°F).
Modes (or standing waves) will occur at 7870 Hz in rooms where two opposing walls (axial mode), edges (tangential mode) or corners (oblique mode) are spaced by a distance d = nλ/2 where:
nis a natural (positive integer greater than or equal to 1)λis the 7870 Hz wavelength = 0.04 meters, or 0.14 feet in air at 20°C (68°F).
7870 Hz Standing Waves Distances
| n | Distance (m) | Distance (ft) |
|---|---|---|
| 1 | 0.02 | 0.07 |
| 2 | 0.04 | 0.14 |
| 3 | 0.07 | 0.21 |
| 4 | 0.09 | 0.29 |
| 5 | 0.11 | 0.36 |
We typically don't treat rooms for standing waves above 300 Hz.
Given the relatively small 7870 Hz half wavelength, you can treat your room by using thick acoustic foam. This will absorb frequencies as low as 250 Hz, and all the way up to 20,000 Hz.
How To Convert 7870 Hz To ms
A Hz (Hertz) is a cycle (or period) per second.
Because a 7870 Hz wave will ocillate 7870 times per second, we can find the time of a single cycle (or period) with the formula p = 1/f where:
fis the frequency of the wave = 7870 Hz
The result will be expressed in seconds, so let's multiply by 1000 to get miliseconds:
1 / 7870 Hz * 1000 = 0.13 ms.