Question

In pipes, why when a standing wave is created does an antinode always form at an open end?

Answer 1

@hartnn @pooja195 @Michele_Laino @jigglypuff314 @Preetha

Answer 2

@vishweshshrimali5 @l

Answer 3

Actually that is because at open ends we need maximum intensity or amplitude...

Answer 4

and that is why there are antinodes at open end and nodes at the fixed ends

Answer 5

Yeah but why actually we need maximum intensity?

Answer 6

@vishweshshrimali5

Answer 7

That is because the displacement in air molecules at open end is max. or if you want to put it in other way i.e. the pressure generated is max. at open end... the more detailed explanation you can get by solving the wave equation DE...

Answer 8

But my main question is why the displacement in air molecules at open end is max?

Answer 9

Well that will be a bit tough for me to answer... but lemme try

Answer 10

Okay so we first thing first... there cannot be an instantaneous change in pressure at the point where atmosphere and pipe meet... right ?

Answer 11

So that means if antinode is going to form it will always have to be antinode and vice versa?
But why cannot there be an instantaneous change?

Answer 12

Because while solving the equation we make an assumption that pressure is constant outside the tube and then use it as a boundary condition for the open end of the tube... Now, of course this is not what that practically happens... but for that we have some correction factors...

Answer 13

Now, if we consider the pressure difference at a point inside the pipe and outside the pipe, then it will be minimum i.e. 0 at the open end... that makes a node for pressure wave... now, when a node of pressure wave occurs, then, there also occurs an antinode for displacement... That is why you get an antinode at the open end

Answer 14

"Now, if we consider the pressure difference at a point inside the pipe and outside the pipe, then it will be minimum"
Wouldn't it be >0 since an antinode is formed at an open end (meaning lowest pressure)

Answer 15

No see when we consider that pressure is constant... then that automatically means that pressure at the open end = pressure outside the pipe ... This makes the pressure difference 0 => minimum => node for pressure wave... and pressure wave and displacement wave follow inverse pattern => antinode for displacement wave at open end

Answer 16

Okay so just last thing why does the pressure difference create an antinode?

Answer 17

The question basically is what does pressure difference have to do with anything?

Answer 18

This you can understand if you take a closer look about how pressure difference leads to the intermolecular movement of molecules of the medium which leads to the displacement wave...

Answer 19

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/imgsou/airphase.gif

Answer 20

Have a look at this figure.. this will explain what I was mentioning about the inverse relationship

Answer 21

Notice the phase difference between pressure variation and air displacement...

Answer 22

Okay but can just enlighten me on that a little?

Answer 23

Yeah sure..

Answer 24

Okay so let's take a closer look at the molecular diagram in the figure..

Answer 25

Can you see how closely the molecules are when there is a pressure antinode...?

Answer 26

Yeah and the opposite is for pressure node

Answer 27

So when molecules are closer they are under compression .. right?

Answer 28

yep

Answer 29

That means high pressure.. thus we have a pressure antinode there..

Answer 30

yes absolutlely

Answer 31

Great! Now, when particles are closer their intermolecular distance is low

Answer 32

That means displacement of sound will be low.. right?

Answer 33

yes

Answer 34

That means a node for displacement wave

Answer 35

displacement of particles from their mean position is what you mean the displacement of sound right?

Answer 36

Yeah...

Answer 37

Yeah I know the fact that high pressure= less volume

Answer 38

In sound's case, since the direction of motion of particles is along the motion of sound, we can directly relate it to the intermolecular distance

Answer 39

less volume = less distance which will create a node for displacement wave

Answer 40

but just explain me the open end part

Answer 41

Okay so you got why when there is a pressure node there will be a displacement antinode?

Answer 42

Now,

Answer 43

Consider this figure... now while solving the wave equation, we make the assumption that pressure outside of the pipe is constant thus at the interface there will be the same pressure P_atm

Answer 44

Now just to the left of interface, we have P_atm pressure and just to the right we have pressure at open end... now, pressure cannot change instantaneously... so, pressure at open end should also be P_atm

Answer 45

Any doubt?