Vibrations of a circular membrane

In summary, the conversation is about understanding the relationship between two sets of figures in a link provided. The first set, Figure 3.6, shows the first 14 modes of an ideal membrane. The second set, titled 'Normal vibration modes of a circular membrane', has figures labeled with J0,J1,J2,J3 and 1,2,3,4. The relationship between these two sets is that the figures in the upper set correspond to specific figures in the lower set, but not all figures are represented in both sets. This is causing confusion for the person asking for help.
  • #1
svishal03
129
1
Hi,

Please can anyone help me here?

Consider the link below;

http://online.physics.uiuc.edu/courses/phys193/Lecture_Notes/P193_Lect4_Ch4_Part2.pdf


I'm just trying to qualitatively undestand the pictures in the above link.

Consider Page 2 of 18

Now, consider figure 3.6

Figure 3.6 shows first 14 modes of an ideal membrane.

Just below figure 3.6 there is another figure titled 'Normal vibration modes of a circular membrane' named as J0,J1,J2,J3 from left to right and 1,2,3,4 from top to bottom.

Can anyone tell me the relationship between the two sets of figures (Figure 3.6 and figures below 3.6?).

Please help
 
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  • #2
J0,1 top left, corresponds to (0,1)
J0,2 corresponds to (0,2) - not shown
J0,3 corresponds to (0,3) - third along second row
and so on...
Not all all the figures in the upper set of diagrams are represented in the lower set, and vice versa. This is what is confusing.
 

1. What is a circular membrane?

A circular membrane refers to a thin, flexible material that is stretched across a circular boundary. It can vibrate and produce sound when excited by an external force, such as a drum head or a cymbal.

2. How do vibrations occur in a circular membrane?

Vibrations in a circular membrane occur when the membrane is struck or excited by an external force. This force causes the membrane to move up and down, creating waves that travel across the surface and produce sound.

3. What factors affect the vibrations of a circular membrane?

The vibrations of a circular membrane can be affected by various factors such as the tension of the membrane, the size and shape of the membrane, and the material it is made of. The type of excitation and the presence of any boundaries can also influence the vibrations.

4. How do you calculate the frequency of vibrations in a circular membrane?

The frequency of vibrations in a circular membrane can be calculated using the equation f = c/2πr, where f is the frequency, c is the speed of sound, and r is the radius of the membrane. This formula applies to the fundamental frequency, or the lowest frequency at which the membrane can vibrate.

5. What are some real-world applications of circular membrane vibrations?

Circular membrane vibrations have various real-world applications, such as in musical instruments like drums and cymbals, as well as in speakers and microphones. They are also used in medical procedures such as ultrasound imaging and in engineering for measuring and detecting structural failures.

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