Standing Wave Frequencies in Wire & Pipe: Similarities & Differences

[PremedBeauty]

-Look up or derive the frequencies of the standing waves of a length of wire, L, clamped at the ends and under tension.
-What are the similarities and differences between a vibrating string and a resonating pipe?
-Does the diameter of the wire matter?
-Does the diameter of the pipe matter?

-first question, I don't know how to derive it.
-The pipe is hollow and the forces acting upon it will be different because the inside is space. The forces will need to overcome the structural strength of the tube.The wire is a solid cylinder. Thus the vibration can travel throughout easier.
-The diameters will make a difference dependent upon the force of the vibration,The diameter of the string also affects the frequency of the string. A thicker diameter vibrates slower, causing the pinch in the string to travel slower. This results in fewer cycles per second, which is a lower frequency so yes.
-I'm thinking the similar answer goes to the pipe as well.

please check these answers.

 

[berkeman]

Moved from Advanced Physics to Intro Physics.

I believe that for the pipe, they are talking about resonance of air standing waves in the pipe, not the pipe bending and resonating itself like a wire does.

And as for the equation that describes waves on a string or wire, you can find that at wikipedia.org or most Intro Physics books under simple harmonic motion (SHM).

 

[m2003]

I would like to clarify and provide additional information on the topic of standing wave frequencies in wire and pipe.

To begin, the frequencies of standing waves in a wire can be calculated using the equation f = nv/2L, where n is the harmonic number, v is the speed of the wave, and L is the length of the wire. The first harmonic, or fundamental frequency, is when n=1 and the wire forms a single loop. The second harmonic, or first overtone, is when n=2 and the wire forms two loops, and so on. These frequencies are dependent on the tension and density of the wire, as well as its length.

Now, to address the similarities and differences between a vibrating string and a resonating pipe. Both systems have fixed ends and are under tension, which allows for standing waves to form. However, the pipe is a hollow cylinder and the forces acting on it are different compared to a solid wire. In a pipe, the air inside the tube also plays a role in the frequency of the standing waves. Additionally, the shape of the pipe can affect the frequencies, as different modes of vibration can occur depending on the diameter and length of the pipe.

This brings us to the question of whether the diameter of the wire or pipe matters. As mentioned earlier, the diameter of the wire can affect the frequency, with thicker wires producing lower frequencies. Similarly, the diameter of the pipe can also influence the frequency of the standing waves. In general, a wider diameter pipe will have lower frequencies compared to a narrower one.

In conclusion, while there are similarities between standing waves in wire and pipe, there are also significant differences due to the nature and structure of the materials. The diameter of both the wire and pipe can impact the frequency of standing waves, but the effects may differ due to the different forces and modes of vibration present in each system. Further research and experimentation can provide a deeper understanding of these phenomena.