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# Relative speed of sound in solids, liquids, and gases

## Video udskrift

- [Voiceover] To change the speed of sound you have to change the properties of the medium that sound wave is traveling through. There's two main factors about a medium that will determine the speed of the sound wave through that medium. One is the stiffness of the medium or how rigid it is. The stiffer the medium the faster the sound waves will travel through it. This is because in a stiff material, each molecule is more interconnected to the other molecules around it. So any disturbance gets transmitted faster down the line. The other factor that determines the speed of a sound wave is the density of the medium. The more dense the medium, the slower the sound wave will travel through it. This makes sense because if a material is more massive it has more inertia and therefore it's more sluggish to changes in movement or oscillations. These two factors are taken into account with this formula. V is the speed of sound. Capital B is called the bulk modulus of the material. The bulk modulus is the official way physicists measure how stiff a material is. The bulk modulus has units of pascals because it's measuring how much pressure is required to compress the material by a certain amount. Stiff, rigid materials like metal would have a large bulk modulus. More compressible materials like marshmallows would have a smaller bulk modulus. Row is the density of the material since density is the mass per volume, the density gives you an idea of how massive a certain portion of the material would be. For example, let's consider a metal like iron. Iron is definitely more rigid and stiff than air so it has a much larger bulk modulus than air. This would tend to make sound waves travel faster through iron than it does through air. But iron also has a much higher density than air, which would tend to make sound waves travel slower through it. So which is it? Does sound travel faster though iron or slower? Well it turns out that the higher stiffness of iron more than compensates for the increased density and the speed of sound through iron is about 14 times faster than through air. This means that if you were to place one ear on a railroad track and someone far away struck the same railroad track with a hammer, you should hear the noise 14 times faster in the ear placed on the track compared to the ear just listening through the air. In fact, the larger bulk modulus of more rigid materials usually compensates for any larger densities. Because of this fact, the speed of sound is almost always faster through solids than it is through liquids and faster through liquids than it is through gases because solids are more rigid than liquids and liquids are more rigid than gases. Density is important in some aspects too though. For instance, if you heat up the air that a sound wave is travelling through, the density of the air decreases. This explains why sound travels faster through hotter air compared to colder air. The speed of sound at 20 degrees Celsius is about 343 meters per second, but the speed of sound at zero degrees Celsius is only about 331 meters per second. Remember, the only way to change the speed of sound is to change the properties of the medium it's travelling in and the speed of sound is typically faster through solids than it is through liquids and faster through liquids than it is through gases.