How does density affect pressure in longitudinal waves?

[rishch]

In my textbook they have introduced the concept of longitudinal waves and go on to explain what a compression and what a rarefaction is.It is written-

"In a compression, there is a temporary increase in the density of the medium; and in a rarefaction,there is a temporary decrease in the density of the medium through which a longitudinal wave passes. When the density of the medium increases, its pressure also increases; and when the density of the medium decreases, then its pressure also decreases."

How? Why does the pressure increase if the density increases?Also what is the pressure they are talking about?Is it the pressure the compression exerts on the surround ing medium or the pressure the surrounding medium exerts on the compression ?

 

[sophiecentaur]

The density will be inversely proportional to the pressure (increase the pressure - squeeze it - and there will be more molecules per unit volume).

In a sound wave, the pressure is changing very fast and can be described by looking at the air as many small volumes of air, next to each other. One of these tiny regions of air can either be compressed with a piston in a cylinder , in an experiment, OR by the pressure of the air around it.
Sound propagates as a wave because of the slight delay involved in compressing each of these small regions. The pressure is 'passed along' through the air, from region to region. The delay is largely due to the time taken for molecules (in constant thermal agitation) to bump into each other and transfer the pressure. Speed of sound is, in fact, higher at high temperatures for this reason because the average speed of molecules is higher.
The loudspeaker (or whatever) supplies a varying pressure on its cone and this varying pressure is passed outwards through the air as a wave. If it weren't for the delay, the speed of sound would be infinite! A very stiff medium like steel has a much much higher speed of sound than air because the pressure is passed along much faster.

 

[rishch]

So the pressure there talking about is the pressure of the surrounding air on the compression ?

 

[sophiecentaur]

Pressure 'works' both ways - inwards on the region of air and outwards on the surrounding air. There is no need to distinguish between the two. It's a bit like the tension is a string. Which end does it act on? Answer -Both.

 

[rishch]

Thanks ! Also,what is 1Hz equal to (as in simpler units like seconds etc) ? My guess is that 1Hz=1/1s because frequency(Hz)=1(no unit)/Time period(s).And how is the pressure be 'passed along' ?

 

[sophiecentaur]

Thanks ! Also,what is 1Hz equal to (as in simpler units like seconds etc) ? My guess is that 1Hz=1/1s because frequency(Hz)=1(no unit)/Time period(s).And how is the pressure be 'passed along' ?

If you squeeze the left hand side then the right hand side pushes on the next bit of air and so on. Same as with a long slinky chain. You wiggle the end (in and out - not side to side) and each coil moves the next with a small delay - giving you a visible wave along its length as the disturbance is 'passed along'.

Yes - 1Hz means one cycle per second. (it used to be called cps)

 

[rishch]

Does on cycle have a unit ?

 

[sophiecentaur]

A cycle has no units (it's just a count) but the Hz has the units of 1/seconds as in 'cycles per second'.

 

[rishch]

Thanks a lot !