Sound diffraction

Dad, when we drove on the highway on the way back from Disneyland yesterday, there was a section with walls on both sides of the road. Those are there to block out the noise from cars, right?

That's right. I drove on the Metropolitan Expressway yesterday, and in some places they've installed sound barriers along the edge of the road to reduce the impact of car noise on surrounding buildings and houses.

How effective are soundproof walls?

That's a difficult question. Let me explain it little by little. Even if you build a sound barrier, the noise doesn't disappear, right? Cars that you can see without the sound barrier can still be heard, albeit at a lower volume, even if the barrier makes them invisible. This phenomenon of sound bending around obstacles is called "sound diffraction." Light cannot bend around obstacles, but sound can bend around obstacles.

It's the same principle as how blocking sunlight or fluorescent light creates a clear shadow, right? But why does sound wrap around things when light doesn't?

Actually, that's the key point. You know that both light and sound are waves, right? Light has a wavelength that's about one millionth the length of sound. The wavelength of light is shorter than one-thousandth of a millimeter, so it's much shorter than the dimensions of things around us. That's why when light hits an object, the other side is cast in shadow. A single strand of hair might not cast a shadow because the light would wrap around it.

So, if sound is 1/1000th of a million times, that's 1000mm, so the wavelength is 1m?

The frequency of a sound with a wavelength of 1 meter is approximately 300 Hz, which corresponds to the average frequency of a woman's voice. The wavelengths of sounds and light that humans hear and see each have a range. I said that light is shorter than 1/1000th of a millimeter, but to be precise, visible light is 0.4 to 0.8 μm, and the seven colors of the rainbow, from red to violet, fall within that range. As I think I mentioned before, the frequency of audible sound is 20 Hz to 20 kHz, which corresponds to a wavelength of 17 mm to 17 m. You know that sound travels about 340 m in one second, right? Since 1 Hz is one vibration per second, the wavelength of a 1 Hz sound is 340 m, 10 Hz is 34 m, and 10 kHz is 34 mm.

I see, because sound waves have long wavelengths, they can wrap around obstacles.

That's true, but while sound has longer wavelengths than light, shorter wavelengths, that is, high-frequency wavelengths, are only a few centimeters to tens of centimeters long. So, with a soundproof wall several meters in size, just like with light, the area behind the wall is in shadow and sound cannot reach you.

I see, I understand. Conversely, low-frequency sounds travel several meters, so they become louder than the dimensions of the wall and can go over the wall and wrap around to the other side, right?

That's right. So even if you install a sound barrier, the low humming sound isn't reduced much, and it's not very effective against low-frequency sounds. However, the noise generated by cars usually has a frequency response that peaks at 2kHz, where the human ear is most sensitive. Sound barriers are effective at frequencies around that range, so they are often used in places with high noise levels, like highways, where there are buildings and houses nearby. When designing a sound barrier, you need to understand the frequency response of the noise at that location and consider how the sound barrier will be effective at the receiving points, such as buildings and houses, in relation to that response. The noise level at the receiving point is determined by environmental standards, which are noise regulations set by the government, and there is a standard that the noise should ideally be kept below that level, so it is necessary to design a sound barrier that does not exceed that standard.