The velocity of sound is maximum in (1) liquids (2) solids (3) gases (4) Cannot be determined

Understanding how sound travels through different mediums is a fascinating exploration into the principles of physics. Sound waves are essentially vibrations that move through mediums by causing particles to bump into each other. This can happen through gases, liquids, and solids. These waves carry energy, which we perceive as sound.

What's particularly interesting is that the speed at which sound travels, or its velocity, varies greatly depending on the medium. In a gas like air, sound waves travel relatively slowly compared to liquids and solids. This is because the particles in gases are more spread out, offering less efficient energy transfer between them. Moreover, in liquids, sound waves travel faster than in gases as the molecules are closer together, facilitating a better transfer of vibrations. However, it's in solids where the true speed of sound shines - particles are tightly packed, making the transfer of sound energy extremely efficient.

Since different mediums affect sound velocity differently, environmental conditions such as temperature and pressure can also play a significant role. For instance, warmer temperatures generally increase the velocity of sound in air due to particles moving more rapidly, enhancing the energy transfer process.

The elastic modulus, often symbolized as 'E', is a measure of a material's ability to resist deformation when a force is applied. Think of it like the stiffness of a spring; the higher the elastic modulus, the stiffer the material and the more it resists deformation.

This physical property is a fundamental factor in determining the velocity of sound through a medium. A higher elastic modulus typically leads to a faster sound velocity since the medium's particles are more rigid, which aids in the quicker transfer of vibration — and hence the sound waves. When the elastic modulus of a medium is high, it can quickly return to its original shape after being disturbed, which significantly enhances the propagation of sound.

In the case of solids, they have the highest elastic modulus among the three states of matter. This high level of stiffness allows them to transmit sound waves the fastest, which is why when you tap on a solid object like metal or stone, the sound seems almost instantaneous.

Density, indicated by the Greek letter 'ρ', refers to how much mass is contained in a given volume of a material. It's an intrinsic property that affects many aspects of sound propagation. A higher density often means that the particles within a material are packed closer together.

Now, where it gets really interesting is in the relationship between density and sound velocity. While you might initially assume that a more dense medium would slow down sound because there's more material to move through, it's actually a matter of how tightly packed the molecules are. The closer together the molecules are, the faster they can transfer vibration from one to another, helping the sound to travel quickly.

However, density alone doesn't tell the whole story. The velocity of sound depends on both the material's density and its elastic modulus. The formula for calculating sound velocity is \( v = \sqrt{\frac{E}{\rho}} \), indicating that while density plays a crucial role, it's the combination with the elastic modulus that determines the true speed of sound in a medium. As seen in solids, a higher density combined with a high elastic modulus means sound can travel exceedingly fast.