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8.

Laws of Vibrating String

Law of length: n µ

1

l

, if T and m are constant

Law of tension: n µ , if l and m are constant

, if l and T are constant

where n:

fundamental frequency of vibration

l:

vibrating length of the string

m:

mass per unit length of the string

T:

tension applied to the string

9.

General Expression for the Frequency of Vibration of a Stretched Wire

n =

p

2l

where p:

number of loops produced along the wire

vibrating length of the wire

mass per unit length of the wire

Fundamental frequency or first harmonic n_{1} =

(p = 1)

Second harmonic or first overtone n_{2} =

= 2n

(p = 2)

10.

Fundamental Frequency of Vibrations of an Air Column in a Tube Closed at One End

n_{1} =

V

4l

, V = velocity of sound in air

l = length of the air column

for first overtone or third harmonic n_{2} =

3V

= 3n_{1}

(only odd harmonics are present)

11.

Fundamental Frequency of Vibrations of an Air Column in a Tube Open at Both Ends

Second mode of vibration = second harmonic

= first overtone n_{2} =

= 2n_{1}

Third mode of vibration = third harmonic

= second overtone n_{3} =

(All harmonics are present)

12.

End Correction

End correction for vibrating air column in resonance tube experiment e = 0.3 d where d: inner diameter of the tube

where l:

length of air column

n:

frequency of tuning fork

length of air column at 1st resonance

l_{1}:

length of air column at 2nd resonance

13.

End Correction to Vibrating Air Column Length in Case of a Pipe Closed at One End

e =

n_{1}l_{1} - n_{2}l_{2}

n_{2} - n_{1}

where l_{1}, l_{2} are the vibrating lengths of the pipe resonating with tuning forks of frequencies n_{1} and n_{2} respectively.

14.

Melde's Experiment

For parallel position, frequency of vibrating string n =

P

Frequency tuning fork: N = 2n For a given N, TP^{2} = constant (for fixed l and m) For perpendicular position, frequency of tuning fork N = n