The speed of sound (Why does sound travel faster in iron?)
Oto-kun
The renovation work in our apartment building has started.
father
Ah, it must be noisy during the day.
Oto-kun
Even though the construction site is quite far from our residence, it sounds like it's happening right next door, doesn't it!?
father
That's because the speed of sound is fast.
Oto-kun
Doesn't sound travel about 340 meters in one second?
father
That is when sound travels in the air.
Oto-kun
Can sound travel through mediums other than air?
father
It was quite a while ago, but we had a conversation about solid propagation sound and air propagation sound, didn't we?
Oto-kun
Ah, I see. The sound that travels through materials like concrete is called solid propagation sound.
father
That's right. I may not have explained this at that time, but the speed of sound varies depending on the medium, such as air, water, or iron.
Oto-kun
I see. Sound can be heard even in the pool, so it travels not only through gases but also through liquids and solids. And how much does the speed of sound differ in those mediums?
father
Look at this table.
Oto-kun
Wow. Sound travels 4 to 5 times faster in water than in air! And about 14 times faster in iron! Why does the speed of sound differ depending on the medium?
father
I don't think you've heard the term "bulk modulus", but the speed of sound can be expressed with this formula in terms of that bulk modulus and density.
1st style
Oto-kun
Bulk modulus?
father
Air is a substance known as an elastic body, which deforms when an external force is applied to it and returns to its original shape once the force is removed. Therefore, when a uniform pressure is applied, it compresses slightly and becomes smaller than its original volume. Let that pressure be p, and let e be the compressed volume per 1 m 3, then p/e is the bulk modulus.
Oto-kun
It seems a bit difficult, but it's the number obtained by dividing the added force by the volume that shrinks (per 1 m 3). Are water and iron also elastic bodies?
father
Ah, it might be hard to imagine, but essentially, the bulk modulus means that a larger number indicates stronger elastic properties. When the same external force is applied, if the change in volume is small, or if a larger external force is required to achieve the same volume change, then the bulk modulus is larger.
Oto-kun
When comparing air and iron, air can undergo volume changes with a smaller force, which means it has a lower bulk modulus.
father
That's right. ① Looking at the formula, in relation to the speed of sound, the fact that the bulk modulus is present in the molecules means that the stronger the elastic properties, the faster the speed of sound. The bulk modulus of air is 1.4 x 10 5 (Pa: Pascal), while that of iron is 1.7 x 10 11 (Pa), which is an order of magnitude different by 10 6.
Oto-kun
However, the speed of sound is determined by the relationship with the density of the denominator.
father
That's right. So, let's compare the densities. The density of air is 1.2 kg/m 3, and iron is 7860 kg/m 3, so it's about 6500 times greater.
From the formula, density is in the denominator, so the greater the density of the medium, the slower the speed of sound, but as the sound says, it's related to the bulk modulus, so as a result, water is about 4 to 5 times faster, and iron is about 14 times faster.
From the formula, density is in the denominator, so the greater the density of the medium, the slower the speed of sound, but as the sound says, it's related to the bulk modulus, so as a result, water is about 4 to 5 times faster, and iron is about 14 times faster.
Oto-kun
I see. That's why the sound of construction seems to be coming from right there.