Question

You blow across the open mouth of an empty test tube and producethe fundamental standing wave of the air column inside the testtube. The speed of sound in air is 344 m/s and the test tube actsas a stopped pipe.

(a) If the length of the air column in the test tubeis 11.0 cm, what is thefrequency of this standing wave?
kHz
(b) What is the frequency of the fundamental standing wave in theair column if the test tube is half filled with water?
kHz

Answer 1

(a). The frequency of this standing wave is 0.782 kHz.

(b). The frequency of the fundamental standing wave in the air is 1.563 kHz.

Step-by-step explanation:

Given that,

Length of tube = 11.0 cm

(a). We need to calculate the frequency of this standing wave

Using formula of fundamental frequency

`f_(1)=(v)/(4l)`

Put the value into the formula

`f_(1)=(344)/(4*0.11)`

`f_(1)=781.81\ Hz`

`f_(1)=0.782\ kHz`

(b). If the test tube is half filled with water

When the tube is half filled the effective length of the tube is halved

We need to calculate the frequency

Using formula of fundamental frequency of the fundamental standing wave in the air

`f_(1)=(v)/(4((L)/(2)))`

Put the value into the formula

`f_(1)=(344)/(4*(0.11)/(2))`

`f_(1)=1563.63\ Hz`

`f_(1)=1.563\ kHz`

Hence, (a). The frequency of this standing wave is 0.782 kHz.

(b). The frequency of the fundamental standing wave in the air is 1.563 kHz.