MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Stationary Waves Formulae Page 2

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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

Law of length: n µ

 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

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

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.

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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