Resonant length and wavelength of sound?

[jnimagine]

hi we did a lab with a resonant tube filled with water
we're supposed to figure out the relationship between the resonant length and the wavelength.
what we did was we filled up the resonant tube with water then put a tuning fork above it and found where that same sound was made.
Here is an example:
frequency of the tuning fork = 1024
1st resonant point:
resonant length: 7.8cm
0.23 ( lamda )
2nd resonant point: 24.5cm
0.72
and so on...

we figured out the resonant length in lamda by finding out velocity of sound in room temperature and finding out lamda by v/f
then resonant length (lamda) was figured out by res. length (cm) / wavelength (lamda)

now i have to figure out the relationship between the resonant length and the wavelength. first is the wavelength here referring to the wavelength figured out by v/f or lamda for resonant length?? is there a relation between the resonant length of the tube and the lamda resonant length?
can someone please help me figure out any kind of relationship here??

 

[Nate810]

The relationship between the resonant length and the wavelength is that the wavelength is equal to the speed of sound in the medium (in this case, room temperature) divided by the frequency of the tuning fork (1024). The resonant length is equal to the wavelength multiplied by the number of half-wavelengths that fit into the tube. So, for example, for the first resonant point, since the wavelength is 0.23, and the resonant length was 7.8 cm, 0.23*7.8 = 1.814, so there were 8 half-wavelengths in the tube.

 

[kyle8921]

I can provide some insights on the relationship between resonant length and wavelength of sound. First, it is important to understand that sound is a type of wave and it travels through a medium, such as air or water. The wavelength of a sound wave is the distance between two consecutive points of the wave that are in phase, or have the same amplitude and direction of motion. In the case of your lab, the tuning fork creates a sound wave that travels through the air and into the resonant tube filled with water.

The resonant length of the tube is the distance between the top of the water and the open end of the tube where the tuning fork is placed. When the tuning fork is struck, it creates a sound wave with a specific frequency, which is the number of cycles per second. This frequency determines the wavelength of the sound wave, and in turn, the resonant length of the tube. As you have observed, the resonant length of the tube changes as the wavelength changes.

To find the relationship between resonant length and wavelength, you can plot your data points (resonant length and wavelength) on a graph and see if there is a pattern or trend. In general, the resonant length and wavelength will have an inverse relationship, meaning that as one increases, the other decreases. This is because a longer wavelength requires a longer resonant length to produce the same frequency of the sound wave.

In terms of the specific relationship between the resonant length of the tube and the wavelength of the sound wave, it can be described by the formula: Resonant length (cm) = n * wavelength (cm), where n is the number of nodes or antinodes (points of maximum displacement) in the sound wave. This means that the resonant length will be a multiple of the wavelength. For example, if there are two nodes in the sound wave, the resonant length will be two times the wavelength.

In summary, the resonant length and wavelength of sound have an inverse relationship, and the resonant length can be expressed as a multiple of the wavelength. I hope this helps you understand the relationship between these two factors in your lab. If you have any further questions, please don't hesitate to ask.