The frequency is directly proportional to length multiplied by tension and mass in the length of string .derive the formula of frequency

Asked by Umeshlochab80 | 12th May, 2021, 09:24: PM

Expert Answer:

Let us start with the following relation for velocity v of standing waves in String under tension T .
 
begin mathsize 14px style v space equals space square root of T over mu end root end style
Where μ is linear mass density of string ,i.e., mass per unit length.
 
If there are n nodes in string of length L , then wavelength λ is given by
 
L = ( n -1 ) ( λ / 2 )  or  λ = ( 2 L ) / ( n - 1 )
 
Let f be the frequency of wave
 
Since we know , velocity v = frequency × wavelength = f × λ 
 
Hence begin mathsize 14px style f space equals space v over lambda space equals space fraction numerator left parenthesis n minus 1 right parenthesis over denominator 2 L end fraction square root of T over mu end root end style

Answered by Thiyagarajan K | 12th May, 2021, 10:38: PM