# Speed of sound in an ideal gas

• greg_rack
In summary, the conversation discussed the calculation of temperature and number of moles for a monoatomic gas using the ideal gas equation and the formula for the speed of sound in a gas. The correct formula was found to be "v = √(γ *p/d)", and further information can be found on the Hyperhysics web page. The conversation concluded with gratitude for the clarification.
greg_rack
Gold Member
Homework Statement
2.0kg of an ideal monoatomic gas(γ = 5/3) are contained inside a box of volume V=4.2m³.
Gas is at a pressure of 3.5bar.

-Calculate sound's velocity through the gas
Relevant Equations
Speed of sound in a gas: ν=√(γkT/m)
IGE: pV=nRT
First of all I thought it was necessary to calculate the temperature(the only data missing for the formula) using the ideal gas equation(since I've already been given 'p' and 'V'), and plug it in the 'v' formula, but the problem immediately occurred when i tried to find out the number of moles(n), that I couldn't manage to find... and that's exactly where I got stuck.

archaic said:
"monoatomic gas" means that your gas is composed of only one atom, or ##n=1##.
That is incorrect. Here n represents the number of moles of the gas present.

There is another formula for the speed of sound in a gas that involves pressure and density. Take a look at the wikipedia article on Speed of Sound.

greg_rack
gneill said:
That is incorrect. Here n represents the number of moles of the gas present.

There is another formula for the speed of sound in a gas that involves pressure and density. Take a look at the wikipedia article on Speed of Sound.
Yes, I have deleted that comment, but somehow you were faster

Last edited:
greg_rack
gneill said:
That is incorrect. Here n represents the number of moles of the gas present.

There is another formula for the speed of sound in a gas that involves pressure and density. Take a look at the wikipedia article on Speed of Sound.

Yeah, you're definitely right... I managed to solve the problem using the wikipedia formula "v = √(γ *p/d)", but I cannot understand why this works since in my physics book the only formula explained is "v = √(γ*k*T/m)", from which i cannot derive the resolving one!

That wikipedia page shows the relationships:

More detail can be found on the Hyperhysics web page for the speed of sound in gases.

greg_rack
You're welcome!

greg_rack

## 1. What is the definition of the speed of sound in an ideal gas?

The speed of sound in an ideal gas is the rate at which a sound wave travels through a medium, such as air, under specific conditions. It is typically measured in meters per second (m/s) and is affected by factors such as temperature, pressure, and molecular weight of the gas.

## 2. How is the speed of sound in an ideal gas calculated?

The speed of sound in an ideal gas can be calculated using the equation c = √(γRT), where c is the speed of sound, γ is the ratio of specific heats for the gas, R is the gas constant, and T is the temperature in Kelvin. This equation is known as the Newton-Laplace equation.

## 3. How does temperature affect the speed of sound in an ideal gas?

As temperature increases, the speed of sound in an ideal gas also increases. This is because as temperature rises, the molecules in the gas move faster and collide more frequently, allowing sound waves to travel more quickly through the medium.

## 4. What is the speed of sound in an ideal gas at room temperature?

At room temperature (around 20°C or 68°F), the speed of sound in air is approximately 343 m/s. However, this value can vary depending on factors such as humidity, altitude, and composition of the gas.

## 5. How does the speed of sound in an ideal gas compare to other mediums?

The speed of sound in an ideal gas is typically slower than in liquids and solids. For example, in air at room temperature, the speed of sound is about 4 times slower than in water and 15 times slower than in steel.

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