Clarity on speed of a longitudinal wave

The direction of propagation of longitudinal waves coincides with the direction of vibration of the medium. They are primarily to blame for the terrifying sounds that accompany large earthquakes. These waves travel at about 5 miles per second and cause the crustal rock to vibrate in the wave’s direction of travel. Because of these vibrations, the rocks push together (compress the blocks) and rip apart (dilate the blocks). Because of their sound, when P waves emerge from deep within the earth, a portion of their energy may be transmitted into the atmosphere as sound waves (Bolt, 1988).

Speed of a longitudinal wave

Longitudinal wave, a wave composed of a periodic disturbance or vibration that occurs in the same direction as the wave’s advance. When a coiled spring is compressed at one end and then released, a wave of compression travels its length, followed by a stretching; any point on any coil of the spring will move with the wave and return along the same path, passing through the neutral position and then reversing its motion. As the sound wave vibrates back and forth, it compresses and expands the gas in the direction of travel of the sound wave. P (primary) seismic waves are also longitudinal in nature.

Each particle of matter vibrates about its normal rest position and along the axis of propagation in a longitudinal wave, and all particles participating in the wave motion behave in the same way, except for a progressive change in phase (q.v.) of vibration—that is, each particle completes its cycle of reaction at a later time. The combined motions cause alternating regions of compression and rarefaction to advance in the direction of propagation.

General Formula for  longitudinal wave

y(x,t)=y0Cos[(t-x/c)]

Where, y is the displacement of the point on the travelling sound wave, and x is the distance travelled from the source of the wave. The amplitude of the oscillations is given by y0. The wave’s speed is given by c. ω is the wave’s angular frequency. x/c( wave takes to travel the distance x).

The wave’s frequency (f) is given by the formula: f = 2 

I hope you understand what a longitudinal wave is and how to calculate it. Let us now go over sound waves and pressure waves in depth.

What is Newton’s formula for Longitudinal wave

The velocity of a longitudinal wave in an elastic medium is given by:

v= √B/p

Where B is the Bulk modulus and is the medium density. We may use this relationship to obtain the formula for the speed of sound across a medium since a sound wave is a longitudinal wave.

Laplace correction

Newton has applied Boyle’s law to pressure changes and volume changes based on Laplace’s assumption of isothermal conditions prevailing when sound travels through air. 

There is a nominal increase in temperature in a compression region and a marginal decrease in temperature in a rarefaction region. According to Laplace, because these pressure changes occur quickly and air is a poor conductor of heat, temperature equalisation among the various regions was improbable. 

The heat generated in the compressed layers is completely confined to these layers and has no time to dissipate throughout the entire body of the object. Similarly, the cold caused in the rarefied layers cannot be compensated for by the flow of heat from other layers inside it.

The corrected formula is 

v=√γp/P

 where  γ=CP/CV

Sound as a longitudinal wave

It was stated that sound is a mechanical wave produced by a vibrating object. The object’s vibrations cause particles in the surrounding medium to vibrate, transporting energy through the medium. The vibrations of the particles in a sound wave travelling through air are best described as longitudinal. Longitudinal waves are those in which the individual particles of a medium move in a direction parallel to the direction of energy transport. A longitudinal wave can be created in a slinky by stretching it out horizontally and vibrating the first coils of the slinky horizontally.

Conclusion

The direction of propagation of longitudinal waves coincides with the direction of vibration of the medium. Longitudinal wave is a wave composed of a periodic disturbance or vibration that occurs in the same direction as the wave’s advance. As the sound wave vibrates back and forth, it compresses and rarefactions the gas in the direction of travel of the sound wave. We may use this relationship to obtain the formula for the speed of sound across a medium since a sound wave is a longitudinal wave. The vibrations of the particles in a sound wave travelling through air are best described as longitudinal. Longitudinal waves are those in which the individual particles of a medium move in a direction parallel to the direction of energy transport.