A 160 g rope 4 m long is fixed at one end and tied to a light string of the same length at the other end. Its tension is 400 N. (a) What are the wavelength of the fundamental and the first two overtones? (b) What are the frequencies of these standing waves? [Hint :In this case, fixed end is a node and the end tied with the light string is antinode.]

A 160 g rope 4 m long is fixed at one end and tied to a light string o

1.	A 160 g rope 4 m long is fixed at one end and tied to a light string of the same length at the other end. Its tension is 400 N. (a) What are the wavelength of the fundamental and the first two overtones? (b) What are the frequencies of these standing waves? [Hint :In this case, fixed end is a node and the end tied with the light string is antinode.]
Answer» SOLUTION :(a) `l = lambda_(1)//4` `:. lambda_(1) = 4l = 16M,l= (3lambda_(2))//4` `:. lambda_2 = (4l)/3 = 5.33m` `l = 5lambda_(3)//4` `:. lambda_3 = (4l)/5 = 3.2m ` (b) `v= sqrt (T/mu)` `= sqrt(400/(0.16//4)) = 100 m//s` Now, `f_1 = v/lambda_1 = 100/16 = 6.25 Hz` Similarly, `f_2` and `f_3`.