Question

In terms of T, mu and l, find frequency of (a) fourth overtone mode (b) third harmonic .

Answer 1

When two end of a string is fixed ,then we can produce vibration in number of ways.This vibration produce ha standing wave which is known as mode of vibration.

(a) In fifth mode of vibration: Consider lamda5 is the wavelength of the wave .Here N=5 ,where N is number of waves which formed on string .

Then L=5/2 lamda5

lamda5=(2L)/5

n5=n/lamda5=(5n)/2L

= 5n1............... (since n1=n/2L)

=5/2L (under root sq T/mu)

Where ,T = tension in string

mu = mass per unit length of string

And this is the frequency of fourth overtone.

(b) similarly, In third mode of vibration : N=3

L=(3 lamda3 )/2

lmada3=(2L)/3

n3=n/lamda3=(3n)/2L

=3n1=3/2L (under root sq.T/mu)

This is the frequency of third harmonic.