How Far Apart Are Two Adjacent Nodes in a Standing Wave?

[Link]

The velocity of waves on a string is 92 m/s. If the frequency of standing waves is 475Hz, how far apart are two adjacent nodes?

W = wavelength

f = v/W


W = 92/475 = 0.194 m

At this stage, I thought the answer was sufficient. However, maybe it is because i don't udnerstand the question, but the book says the answer should be 0.097m. The only way I could achieve this was to:

L = W/2 = 0.194 / 2 = 0.097m

This should then be a first harmonic wave. I am wondering:

Isnt the distance bewteen two adjacent nodes simply the wavelength?
Why should I divide it by 2, and when does the question imply it is talking about a first harmonic wave?

Thank you

 

[Galileo]

A node is a point where there is no displacement. Just look at the sine wave, it has two zero's in one period, so there are two nodes in a wavelength.

 

[Link]

ah i see! Thx!

 

[misskitty]

Link are you all set now or are you still wondering why the length between the nodes is not the wave length?

Kitty

 

[dextercioby]

The problem is rather ambiguous.It says nothing about the appearance of those waves.They need't be periodic,nor sinusoidal,just solutions of the d'Alembert equation.

Daniel.

 

[The Bob]

Well not really. It says it is a standing wave, must have to fixed points. I says what the frequency of that wave is and what speed the wave is traveling at. This means the wavelength can be worked out and in all standing waves (of the sort Link's mentions) you then divide by two to find the distance between the nodes.

The Bob (2004 ©)

 

[kusal]

The answer given is correct it's= 0.09684m
The wave length of a standing wave is equal to (distance between the two nodes*2)

Think how standing waves are made (by interference of two periodic waves).then you would be able to figure thi out.note that node is the place where the pressure is highest and that there are two such places in a beat.

 

[comwiz72]

...^......
.../...\.....
../...\......
/...\....
...\.../...
....\.../...
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.....V...

Your standing wave - the distance between the nodes, is either one peak or one trough as above - aka half a wavelength.


Just wanted to use some ASCII art there to clarify the point some :-)


EDIT:::
Sorry had to add dots as ASCII spaces were removed