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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Stationary Waves Formulae Page 2

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laws of vibrating string

 8.

Laws of Vibrating String

 

Law of length: n

1

l

, if T and m are constant

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

Law of length: n

1

, 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

Frequency of Vibration of a Stretched Wire

 

9.

General Expression for the Frequency of Vibration of a Stretched Wire

 

n =

p

2l

 

where p:

number of loops produced along the wire

l:

vibrating length of the wire

m:

mass per unit length of the wire

T:

tension applied to the string

 

second harmonic or first overtone n2

Fundamental frequency or first harmonic n1 =

1

2l

 

(p = 1)

 

 

 

Second harmonic or first overtone n2 =

1

2l

= 2n

(p = 2)

 

 

 

 

10.

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

 

n1 =

V

4l

, V = velocity of sound in air

 

l = length of the air column

 

for first overtone or third harmonic n2 =

3V

4l

= 3n1

(only odd harmonics are present)

 

11.

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

 

n1 =

V

2l

, V = velocity of sound in air

 

l = length of the air column

Second mode of vibration = second harmonic

= first overtone n2 =

V

2l

= 2n1

Third mode of vibration = third harmonic

= second overtone n3 =

3V

2l

= 3n1

(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

  1. Velocity of sound V = 4n (l + 0.3 d)

where l:

length of air column

n:

frequency of tuning fork

  1. Velocity of sound (eliminating end correction)
    V = 2
    n (l1 - l)

where n:

frequency of tuning fork

l:

length of air column at 1st resonance

l1:

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 =

n1l1 - n2l2

n2 - n1

where l1, l2 are the vibrating lengths of the pipe resonating with tuning forks of frequencies n1 and n2 respectively.

Melde's Experiment

 

14.

Melde's Experiment

 

For parallel position, frequency of vibrating string n =

P

2l

Frequency tuning fork: N = 2n
For a given N, TP2 = constant (for fixed
l and m)
For perpendicular position, frequency of tuning fork N =
n

 

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