Question

(a) What length of pipe open at both ends has a fundamental frequency of 3.75 102 Hz?

Find the first overtone.

lpipe = .457 Incorrect: m

fovertone = 750 Correct: Hz

(b) If the one end of this pipe is now closed, what is the new fundamental frequency?

Find the first overtone.

ffundamental = 750 Incorrect: Hz

fovertone = 615 Incorrect: Hz

(c) If the pipe is open at one end only, how many harmonics are possible in the normal hearing range from 20 to 20000 Hz?

n =

Answer 1

here,

a)

speed of sound , v = 343 m/s

let the wavelength be lamda

frequency , f = 375 Hz

lamda= v/f

lamda = 343 / 375

lamda = 0.915 m

length of pipe , l= lamda/2 = 0.46 m

b)

new wavelength ,W' = 4*L

W' = 1.83 m

new fundamental frequency , f' = c/w' = 187.5 Hz

the new fundamental frequency is 187.5 Hz

wavelength of overtone , w = l/0.75

w = 0.61 m

frequency of overtone , fo = 343/0.61

fo = 559.24 Hz

c)

number of harmonices , n = 20000/187.5

n = 106.67 = 106

the number of harmonics are 106