# Sound Waves     ## What Is a Sound Wave?

The acoustic wave is a pattern of disturbance which occurs by the movement of energy traveling through a medium (like air, water, or the other liquid or solid matter). The source is a few objects that cause vibration, like a ringing telephone, or an individual's vocal cords. The vibration disturbs the particles within the surrounding medium; those particles disturb those next to them, and so on. The pattern of the disturbance creates an outward movement at the time of a wave pattern. The wave carries the sound energy through the medium, usually altogether directions and fewer intensely as it moves farther from the source.

## Speed of Sound Waves in Solids, Liquids, Gases

### Newton’s Formula for Speed of Sound Waves:

Newton showed that the speed of sound during a medium

v = $\sqrt{E}{P}$

E = Modulus of elasticity of the medium

P = The density of the medium.

### Speed of Sound Waves in Solids

v = $\sqrt{P}{Y}$

Y = Young’s modulus of the solid

P = Density of the solid

### Speed of Sound Waves in Liquid

v = $\sqrt{P}{B}$

B = Bulk modulus of the liquid

P = Density of the liquid

### Speed of Sound Waves in Gases

Newton considered the propagation of sound waves through gases as an isothermal process PV = constant (as the medium is into getting heated when sound is passing through it.), then he stated:

v=√γ/ρ

P is Pressure of the gas (isothermal Bulk modulus of gas) there was a huge discrepancy in the speed of sound determined by using this formula with the experimentally determined values. Hence, a correction to this formula was given by Laplace; it is known as Laplace correction.

### Laplace Correction

According to Laplace, the propagation of sound waves in gas occurs adiabatically. So the adiabatic coefficient of elasticity of the gas (γP) has got to be used hence the speed of sound waves within the gas:

V = $\sqrt{P / \gamma P}$

γP – Adiabatic bulk modulus of the gas

P – The density of the medium

The values obtained by Newton – Laplace formula is in excellent agreement with the experiment results.

## Factors Affecting the Speed of Sound in Gases

• Effect of pressure

• Effect of temperature

• Effect of density of the gas

• Effect of humidity

• Effect of wind

• Effect of change in frequency (or) wavelength of the acoustic wave

• Effect of amplitude

### Effect of Pressure

If the pressure is increased at a constant temperature by Boyle’s law

PV = constant [for a hard and fast mass of gas]

P = density of the gas (for the fixed value of density)

P/P = constant

So change in pressure doesn't affect the speed of sound waves through a gas.

### Effect of Temperature

Temperature is additionally a condition that affects the speed of sound. Heat, like sound, maybe a type of mechanical energy. Molecules at higher temperatures have more energy, thus they'll vibrate faster. As the molecules vibrate faster, sound waves travel more quickly. The speed of sound is temperature air is 346 meters per second.

### Effect of Humidity

Under the same conditions of temperature and pressure, the density of water vapor is less than that of dry air in the presence of moisture decreases the effective density of air,  hence the acoustic wave travels faster in moist air than in dry air.

### Effect of Wind

Wind simply adds its velocity vectorially to that of the acoustic wave, if the component of Vw of wind speed is within the direction of the acoustic wave, the resultant speed of sound is

V resultant = V + Vw

Vw – wind speed

### Effect of Change in Frequency (or) Wavelength of the Acoustic Wave

Change of frequency (or) wavelength does not affect the speed of sound in a medium (Homogeneous isotropic medium). Sound travels at the same speed in all directions.

V = λF = constant

When an acoustic wave passes from one medium to a different medium, the frequency remains constant but wavelength and velocity changes.

### Did You Know?

The sound may be a mechanical wave that results from the rear and forth vibration of the particles of the medium through which the acoustic wave is moving. If an acoustic wave is moving from left to throughout air, then particles of air are going to be displaced both rightward and leftward because the energy of the sound wave passes through it. The motion of the particles is parallel to the direction of energy transport. This characterizes sound waves in air as longitudinal waves. A sound is a form of energy arising due to mechanical vibrations.

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