Standing sound waves are produced in a pipe that is 2.20 m long. B) If the pipe

Question

Standing sound waves are produced in a pipe that is 2.20 m long.

B) If the pipe is open at both ends, determine the locations along the pipe (measured from the left end) of the displacement nodes for the first overtone. [ x = ____ m ]

C) If the pipe is open at both ends, determine the locations along the pipe (measured from the left end) of the displacement nodes for the second overtone. [ x = ____ m ]

D) If the pipe is closed at the left end and open at the right end , determine the locations along the pipe (measured from the left end) of the displacement nodes for the fundamental frequency. [ x = ____ m ]

E) If the pipe is closed at the left end and open at the right end , determine the locations along the pipe (measured from the left end) of the displacement nodes for the first overtone. [ x = ____ m ]

F) If the pipe is closed at the left end and open at the right end , determine the locations along the pipe (measured from the left end) of the displacement nodes for the second overtone. [ x = ____ m ]

Explanation / Answer

B) opened at both ends

for 1st overtone frequency the corresponging wavelength lamda = l = 2.2 m

from the left end the displacement node located at lamda/4,3lamda/4 then 2.2/4 and 3*(2.2/4)

x= 0.55 m and 1.65 m

C) for the second overtone lamda = (2*l/3) = 2*2.2/3 = 1.46 m

locations of nodes are 1.46/4 ,3*1.46/4,5*1.46/4

x = 0.36m,1.1m,and 1.8 m

D) for the fundamnetal frequency lamda = 4*l = 4*2.2 = 8.8 m

x = 0 m

E) for the 1st overtone lamda = 4l/3 = 4*2.2/3 = 8.8/3 = 2.93 m

x = 0m,2.93/2m = 0m,1.465 m

F) fror 2nd overtone

lamda = 5*l/4 = 5*2.2/4 = 2.75 m

then x = 0m,2.75/2,2.75 = 0m , 1.375 m , 2.75 m

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