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

In summary, the velocity of waves on a string is 92 m/s and the frequency of standing waves is 475Hz. The distance between two adjacent nodes in a first harmonic wave can be calculated by dividing the wavelength by 2, which results in a distance of 0.097m. This is because a standing wave has two nodes in one wavelength, which is equal to the distance between the two nodes multiplied by 2. The appearance of standing waves may vary, but the concept of nodes and the relationship between wavelength and distance between nodes remains the same.
  • #1
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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 = Wavelenght

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 wavelenght?
Why should I divide it by 2, and when does the question imply it is talking about a first harmonic wave?

Thank you
 
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  • #2
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.
 
  • #3
ah i see! Thx!
 
  • #4
Link are you all set now or are you still wondering why the length between the nodes is not the wave length?

Kitty
 
  • #5
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.
 
  • #6
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 ©)
 
  • #7
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.
 
  • #8
...^......
.../...\.....
../...\......
/...\....
...\.../...
....\.../...
......\.../...
.....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
 
Last edited:

1. What is the formula for calculating the velocity of a standing wave?

The formula for calculating the velocity of a standing wave is v = λf, where v is the velocity, λ is the wavelength, and f is the frequency of the wave.

2. How does the tension of the medium affect the velocity of a standing wave?

The velocity of a standing wave is directly proportional to the tension of the medium. This means that as the tension increases, the velocity of the wave also increases.

3. Can the velocity of a standing wave be altered by changing the amplitude of the wave?

No, the velocity of a standing wave is not affected by changes in amplitude. It is solely determined by the properties of the medium, such as tension and density.

4. What is the relationship between the velocity of a standing wave and the number of nodes?

The velocity of a standing wave is inversely proportional to the number of nodes. This means that as the number of nodes increases, the velocity of the wave decreases.

5. How does the velocity of a standing wave differ from the velocity of a traveling wave?

The velocity of a standing wave is dependent on the properties of the medium, while the velocity of a traveling wave is determined by the properties of both the medium and the source of the wave. Additionally, standing waves have a fixed velocity, while traveling waves can vary in velocity.

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