Question

Standing sound waves are produced in a pipe that is 1.80 m long.

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.

If there is more than one value, separate your answers with commas.

x=

m

SubmitMy AnswersGive Up

Incorrect; One attempt remaining; Try Again

Part 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.

If there is more than one value, separate your answers with commas.

x=

m

SubmitMy AnswersGive Up

Incorrect; Try Again; 5 attempts remaining

Part 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.

If there is more than one value, separate your answers with commas

Answer 1

Displacement node is a point where the displacement is minimum [zero]. For a pipe close from the left end, the displacement node for the fundamental frequency will be: x = 0m.

and since there must be an antinode at the open end of the pipe therefore for the fundamental frequency, this is the only displacement node.

For the 1st overtone, 3/4 of a full wavelength can be fit into the pipe.

so,

=>

Now the first fundamental displacement node will remain at x = 0. There will be another one at .

therefore x = [0, 1.2]

for the 2nd overtone, 5/4 of a wavelength can be fit into the pipe.

so,

=>

as before, the first fundamental displacement node will be at x = 0

there will be one node at and another one at

so, x = [0, 0.72, 1.44].