The relationship between mass and frequency of sound waves in air can be explained through the concept of the speed of sound. The speed of sound in a medium (such as air) is determined by the properties of that medium, including its density and elasticity.
In general, the speed of sound is given by the formula:
v = √(γ * P / ρ)
where: v is the speed of sound, γ (gamma) is the adiabatic index (a constant that depends on the specific heat ratio of the gas), P is the pressure of the medium, and ρ (rho) is the density of the medium.
From this formula, we can see that the speed of sound is inversely proportional to the square root of the density of the medium. Therefore, if the density of the medium increases, the speed of sound decreases.
Now, let's consider a sound wave in air. Sound waves are oscillations of pressure that propagate through a medium, such as air. The frequency of a sound wave is the number of cycles or vibrations per unit of time. In other words, it represents how many compressions and rarefactions occur in a given time.
The relationship between mass and frequency of sound waves can be understood as follows:
Higher mass: If the mass of the air molecules increases, the density of the medium increases. As mentioned earlier, the speed of sound is inversely proportional to the square root of the density. Therefore, if the density increases, the speed of sound decreases. As a result, the frequency of the sound wave also decreases.
Lower mass: If the mass of the air molecules decreases, the density of the medium decreases. This leads to an increase in the speed of sound, and consequently, an increase in the frequency of the sound wave.
In summary, the relationship between mass and frequency of sound waves in air is that an increase in mass (resulting in higher density) leads to a decrease in frequency, while a decrease in mass (resulting in lower density) leads to an increase in frequency. This relationship is derived from the speed of sound formula and the understanding that density affects the propagation speed of sound waves.