You blow across the open mouth of an empty test tube and produce the fundamental standing wave of the air column inside the test tube. the speed of sound in air is 344 m/s and the test tube acts as a stopped pipe. if the length of the air column in the test tube is 15.0 cm , what is the frequency of this standing wave? what is the frequency of the fundamental standing wave in the air column if the test tube is half-filled with water?

Explanation:

In a stopped pipe, which acts as closed organ pipe , standing waves are produced . In fundamental mode of vibration, the length of pipe L is related with the wave length of sound produced as follows .

λ / 4 = L

λ = 4 L

Frequency n = V / λ

= V/ 4L

= 344 / 4 X .15

= 573.33 Hz

When the test tube is half filled with water

length of tube is half sized

L =0.15/2 = .075

n = V/ 4L

344 /4 X 0.075

=  1146.66 Hz.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

inverse v=i*r

nice nice