The speed of sound (Why does sound travel faster inside iron?)
Otokun
Renovation work has started on our apartment building.
father
Ah, it's probably noisy during the day.
Otokun
The construction site is quite far from my apartment, but it sounds like they're working right next door, doesn't it?!
father
That's because sound travels very quickly.
Otokun
Wait, I thought sound travels about 340 meters per second?
father
That's when sound travels through the air.
Otokun
Can sound travel through means other than air?
father
It was quite a while ago, but we talked about structure-borne sound and airborne sound, didn't we?
Otokun
Oh, right. Sound that travels through concrete and similar materials is called structure-borne sound.
father
That's right. I might not have explained it at the time, but the speed at which sound travels differs depending on the medium, such as air, water, or iron.
Otokun
I see. Sound can be heard even in a swimming pool, so sound travels not only through gases, but also through liquids and solids. And how much does the speed at which sound travels differ depending on the medium?
father
Take a look at this table.
Otokun
Wow. Sound travels 4 to 5 times faster in water than in air! And about 14 times faster in iron! Why does the speed at which sound travels differ depending on the medium?
father
You probably haven't heard the term "bulk modulus," but the speed of sound can be expressed using this formula, based on its bulk modulus and density.
① Formula
Otokun
Bulk modulus?
father
Air is an elastic material, meaning that when an external force is applied to an object, it deforms, and when the force is removed, it returns to its original shape. Therefore, when a uniform pressure is applied, it is compressed slightly, becoming smaller than its original volume. If the pressure is p and the compressed volume per 1 m³ is e, then p/e is the bulk modulus.
Otokun
It sounds complicated, but it's basically the force applied divided by the volume compressed by that force (per cubic meter). Are water and iron also elastic?
father
Ah, it might be hard to visualize, but basically, the larger the bulk modulus, the stronger the elastic properties. When the same external force is applied, if the volume change is small, or if a larger external force is needed to bring about the same volume change, the bulk modulus will be large.
Otokun
Comparing air and iron, air can undergo volume changes with less force, which means its bulk modulus is smaller.
father
That's right. ① Looking at the formula, in relation to the speed of sound, the bulk modulus is in the numerator, which means that the stronger the elastic properties, the faster the speed of sound. The bulk modulus of air is 1.4 x 10⁵ (Pa: Pascals), while that of iron is 1.7 x 10¹¹ (Pa), a difference of 10⁶ orders of magnitude.
Otokun
But the speed of sound is determined by its relationship to the density in the denominator, right?
father
That's right. So let's compare the densities. The density of air is 1.2 kg/ m³, and the density of iron is 7860 kg/ m³, so it's about 6500 times denser.
From equation ①, density is in the denominator, so the higher the density of the medium, the slower the speed of sound. However, as Oto said, it's related to the bulk modulus, so as a result, the speed of sound is about 4 to 5 times faster in water and about 14 times faster in iron.
From equation ①, density is in the denominator, so the higher the density of the medium, the slower the speed of sound. However, as Oto said, it's related to the bulk modulus, so as a result, the speed of sound is about 4 to 5 times faster in water and about 14 times faster in iron.
Otokun
I see. That's why the construction sounds like they're happening right there.