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Vibration of a String

Fundamental frequency, 30662.png
 
33927.png
Fig. 14
 
General formula: 30500.png
 
where L = Length of string, T = tension in the string, m = mass per unit length (linear density), and p = mode of vibration.
  
Some Important Points
  • As a string has many natural frequencies, so when it is excited with a tuning fork, the string will be in resonance with the given body if any of its natural frequencies concides with the body.
  • n ∝ 1/L if T and m are constant, 33994.png ifL and m are constant, 33988.png if T andL are constant.
  • If M is the mass of the string of lengthLm = M/L.
     
    So 35066.png
     
    35062.png
     
    where m = πr2ρ (r = radius, ρ = density)
 
Table 2. Comparative Study of Stretched Strings, Open Organ Pipe, and Closed Organ Pipe
 
S. No.
Parameter
Stretched string
Open organ pipe
Closed organ pipe
1.
Fundamental frequency or 1st harmonic
30444.png
30438.png
30430.png
2.
Frequency of 1st overtone or 2nd harmonic
n2 = 2n1
n2 = 2n1
Missing
3.
Frequency of 2nd overtone or 3rd harmonic
n3 = 3n1
n3 = 3n1
n3 = 3n1
4.
Frequency ratio of overtones
2 : 3 : 4…
2 : 3 : 4…
3 : 5 : 7…
5.
Frequency ratio of harmonics
1 : 2 : 3 : 4…
1 : 2 : 3 : 4…
1 : 3 : 5 : 7…
6.
Nature of waves
Transverse stationary
Longitudinal stationary
Longitudinal stationary




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