Sound waves in gases, Mechanical Engineering

Sound Waves in Gases

Sound waves are longitudinal pressure waves. Let us consider the motion of a plane sound wave moving along X-axis in a gas medium. In undisturbed position, the gas medium is described by its equilibrium pressure P0 and density ρ0. A mechanical disturbance deforms the equilibrium state of the gas. The gas particles are displaced longitudinally causing compressions and rarefactions. Consequently, the density and pressure of the gas changes. The pressure variation moves in the medium from one region to the other producing a pressure wave.


To obtain the wave equation, we consider the motion of a thin slab of the gas (of unit area), lying between position x and x + Δ x. Following the steps exactly as in the elastic rod, the average volume strain of this element of gas is given by

230_download.png 

The volume strain is produced because the pressures along the X-axis on both sides of the thin element are different. The net pressure or stress on the gas element, within linear approximation, towards +ve X-axis is

1721_download (1).png 

Now (instead of Young's modulus), the elastic property of gas is defined in terms of its bulk modulus K as

1873_download (2).png 

The minus sign in the definition of K appears because volume strain is negative for positive stress.

1035_download (3).png 

That is, bulk modulus K is determined about equilibrium condition. Hence the net force on the gas element is

1815_download (5).png 

The equation of motion of the gas element (mass = ρ0 Δ x), therefore, is

2383_download (6).png 

Hence, the velocity of sound waves in a gaseous medium

448_download (7).png 

depends upon the equilibrium density ρ0 and bulk modulus K of the gas. Note that bulk modulus K is also evaluated at equilibrium condition

791_download (8).png 

The value of K therefore depends on how pressure of the gas changes with respect to volume during wave motion. It turns out that the temperature in a sound wave does not remain constant. The excess pressure causing the compression raises the temperature of gas there; the region of rarefaction cools slightly as the pressure falls. The time period of oscillation is so small that before heat could flow from one region to another, the region of compression turns into region of rarefaction and vice-versa. The sound motion therefore is an adiabatic process and gas obeys the equation.

178_download (9).png

Posted Date: 9/18/2012 1:51:44 AM | Location : United States







Related Discussions:- Sound waves in gases, Assignment Help, Ask Question on Sound waves in gases, Get Answer, Expert's Help, Sound waves in gases Discussions

Write discussion on Sound waves in gases
Your posts are moderated
Related Questions
Battery: Battery is a device that produces direct current (DC). The chemical energy of battery ingredients converts into electrical energy in the form of direct current. This is a

this is a problem for designing wrecking crane. there are 2 scenarios, one is when ball is held and one where its at maximum. i calculated the loads and now need to find the follow

a) Describe and illustrate the terms with their classification: Mechanism, Kinematic, Machine links and Kinematic pair. b) Discuss the Inversions of double slider crank chain an

Traveling at a speed of 16.0 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of kinetic friction between the tires and the roa

Q.  A steel bar 10 cm broad and 8 mm thick is subjected to bending moment. The radius of the neutral surface is 100 cm. Found out the maximum and minimum bending stress in beam.

Advantage of Electro Chemical Machining 1. As the tool does not come in contact with the work there for tool wear is practically nil. 2. The metal removal is faster rate.

(a) Evaluate the natural frequency of system shown in figure and show that it will be equal to (b) calculate equivalent stiffness of two springs connected in parallel.

Aspects Of Scheduling  The difficulty is a modification of a flexible manufacturing cell at ABB's plant for the manufacturing of turbocharger in Baden, Switzerland. The difficu

Special Casting Methods: 1. Die casting : Die casting is a permanent mould casting techniques in which molten metal is forced in the mould cavity under a pressure of 700 to

Combustion Chamber ( or Clearance Volume ) : Combustion chamber is a space between the cylinder head and the piston top when the piston is at top dead center (TDC). The combustio