Question

A 40-cm-long tube has a 40-cm-long insert that can be pulled in and out. A vibrating tuning fork is held next to the tube. As the insert is slowly pulled out, the sound from the tuning fork creates standing waves in the tube when the total length L is 41.4cm ,55.2cm , and 69.0cm .

What is the frequency of the tuning fork? The air temperature is 20?C.

Answer 1

L1 = 41.4

L2 = 55.2

L3 = 69

in a open pipe

length of the pile = L = n*lambda/2

n = 1,2,3, .....

lambda = 2L/n

frequency f = v/lambda

v = speed of sound in air = 331+(0.6*t) = 331+(0.6*20) =
343 m/s

frequency is same at all the lengths

let at L1 length it is in n mode , at L2 in (n+1)mode, L3 (n+2) mode

f = v/lambda = n*v/2L1 = (n+1)*v/2L2 = (n+3)*v/2L3

n/(n+1) = L1/L2

n/(n+1) = 41.4/55.2

n = 3

f = (3*343)/(4*0.414)

f = 621.4 Hz <--------answer