Vibration of a String
Fundamental frequency,
Fig. 14
General formula:
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, ifL and m are constant, if T andL are constant.
 If M is the mass of the string of lengthL, m = M/L.
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




2.

Frequency of 1st overtone or 2nd harmonic

n_{2} = 2n_{1}

n_{2} = 2n_{1}

Missing

3.

Frequency of 2nd overtone or 3rd harmonic

n_{3} = 3n_{1}

n_{3} = 3n_{1}

n_{3} = 3n_{1}

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
