(ii) Law of tension: , where L and m are constants.
(iii) Law of mass: or
, where L and T are constants.
(iv) Law of radius: n 1/r or n1/n2 = r2/r1, where d, L and T are constants.
(v) Law of density: or , where r, T and L are constants.
On the basis above laws the formulac of frequency of vibration of string are.
M being the mass hanged on string.
16.Melde's experiment:
(i) In a vibrating string of fixed length, the product of number of loops in a vibrating string and squar root of tension is a constant or
= constant.
(ii) n =
(iii) In longitudinal vibration system the frequency of tuning fork.
= 2 X (vibration frequency of string)
(iv) In this experiment vibration of string are always transverse, but in longitudinal vibration system the vibration of arms of the tuning fork are along the direction of string. This experiment is also based on the stationary (transverse) waves.
17. Vibration of air calumns in pipes:
The pipe which cantains air and in which Round vibration are produced , is called organ pipe
(i)Closed pipe :
(a) One and of the pipe of whis kiknd is closed aqnd the other and is open .
(b) Node is formed at closed and end and artinode at the open end . In this pipe, number of artinodes
and nodes are the same.
(c)Closed end of pipe reflects the compression as compression & rarefaction as rarefaction . Open end of
the pipe reflects compression as rarefaction while rarefaction as compression.
(d)For a pipe of length L, the frequency of fundamental note of stationary waves produced.Fundamental frequency 'n', is same as first harmonice,while other are multiple of his frequency (2n,3n,etc.)
, wavelength
. Frequency of third harmonic or the first overtone. wavelength Frequency of the second overtone or the fifth harmonic. as a sompression .Here the number of antinodes is more that of nodes. (b)For a pipe of length L, the frequency of fundamental note and wavelengthMbr /> First overtone ar second harmonic frequency wavelength
Second overtone ar third harmonic frequency Wavelength
These are shown in the following figure:
wavelength These are shown in the following figure:
(a)Fundamental note ar first harmonic (n,)
(b)First overtone ar third hormonic (3n,)
(c)Second ovewtone ar fifth hormonic(5n,)
Therefore the ratio of overtione is 3:5:7.
(e)It is clear that the only add harmonic are produced in this pipe:
n1:n2:n5:....... = 1:3:5........
(ii) Vilrations of an open pipe :
(a) These pepes are open at both ends where antinodes are formed . At these ends copression is
reflected as rarefaction while rarefaction
(d) Fundamental note ar first harmonic (n,)
(e)First overtone ar second harmonic (2n,)
(f)Second overtone ar third harmonic(3n,)
(c)Clearly , in 'open pipe all the harmonics are produced . The ratio of the frequencies is :
n1:n2:n3:....... = 1:2:3........
In this condition the ratio of wvertone is
2 : 3 : 4 : 5 : .........
End correction : e = 0 . 6r where 'r'is the radius of pipe . Therefore for a closed pipe the effective
length of the air column=L+e=L+0.6r.
For open pipe tje effective length of the air column = L + 2e = L + 1.2r.
For a closed pipe with end correction .,
n = v/L+e and for open pipe ,
n = v/2 (L+e)
By Comparesion:
(i)nopen pipe = 2nclosed pipe
(for fundamental only)
(ii)In open pipe all the harmonic are obtained while in closed pipe only add harmonics are obtained.
(iii) The second produced in open organ tube is pleasing & that of the closed organ tube is less pleasing .
(18) Resonance tube:
Resonance : If the frequency of a turnig fork used is same as the frequency of vibration of air column in the
tube, then the intercity of sound becomes maximum. This is said loss the condition ofresonance.
(i) It is an exangle of a closed pipe in which
the length of theair colunn can be changed by adjusting the level of water.
where T and m are constants.
, where L and m are constants.
or 
, where L and T are constants.
1/r or n1/n2 = r2/r1, where d, L and T are constants.
or 
, where r, T and L are constants.
= constant.
, wavelength 
wavelength 
Frequency of the second overtone or the fifth harmonic. as a sompression .Here the number of antinodes is more that of nodes. (b)For a pipe of length L, the frequency of fundamental note 
and wavelength
Mbr /> First overtone ar second harmonic frequency 
wavelength
Wavelength
wavelength
These are shown in the following figure:
