String vibration fixed ends, Mechanical Engineering

String Vibration Fixed Ends

In case of the vibrations of a string, both its ends at x = 0 and x = L may be permanently fixed; y (x = 0) = 0, and y (x = L) = 0at all t. That gives,


For all tA ( x ) = 0 at x = 0, and therefore we have B = 0. Hence, we get

A ( x ) = A sin kx

Also A ( x ) = 0 at x = L; hence, A sin kL = 0

or, kn L = n π         n = 1, 2, .....

1724_download.png 

The above equation gives frequencies of various possible normal modes of a system at both ends. For the string v =  348_download (6).png .

In terms of linear frequency, we write

1906_download (2).png 

For n = 1, the frequency  2319_download (3).png  is called the fundamental; it is the minimum frequency for a normal mode. The higher modes are called harmonics, i.e. vn = n v1 represents nth harmonic. (The fundamental is first harmonic.)

The wavelength λn in nth mode is given by

  1608_download (4).png 

That is, the nth accommodates exactly n/2 wavelength in length L of the medium.

The solution is now written as

933_download (5).png

Posted Date: 9/18/2012 1:38:47 AM | Location : United States







Related Discussions:- String vibration fixed ends, Assignment Help, Ask Question on String vibration fixed ends, Get Answer, Expert's Help, String vibration fixed ends Discussions

Write discussion on String vibration fixed ends
Your posts are moderated
Related Questions

Write short notes on following terms:- (i) Total quality management (ii) Method study (iii) Selective Inventory Control (iv) Break Even analysis (v) Merits Rating an

Q. What is Clad plate and overlay welding? Strip back cladding on clad plate a minimum of 5 mm (3/16") from the edges of weld preparation before welding on the backing plate.

Draw and also explain the stress strain diagram for the following materials a) Copper b) Ductile Materials c) Rubbers and Elastomers and d) Brittle materials.

Q. Show Construction Subcontractor Responsibilities? The Supplier or Construction Subcontractor is responsible for: • Employing qualified PMI technicians • Performing PMI

A horizontal line ABCD measuring 9m is acted upon by forces of magnitude 400, 600, 400 and 200 N at points A, B, C, D respectively with downward direction. These point are so locat

I want to make a form tool for lathe for making a convex groove of 3 mm radius. tool material will be tungsten carbide. I want to know the dimensions of tool. What is the procedure

Like&unlike forces

Separator:   Separator works as insulator between positive and negative plates. These separators are placed between each pair of plates.

Which three principal possible in radial drilling machine Between them the plain drill machine, three principal movements are possible in this type of machine, by vertical move