Question

Unless indicated otherwise, assume the speed of sound in air to be v = 344 m/s. 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. Required:a. If the length of the air column in the test tube is 14.0 cm, what is the frequency of this standing wave? b. What is the frequency of the fundamental standing wave in the air column if the test tube is half filled with water?

Answer 1

a

`f = 614.3 \ Hz`

b

`f_h = 1229 \ Hz`

Step-by-step explanation:

From the question we are told that

The speed of sound in the air is
`v_s = 344 \ m/s`

The length of the test tube is
`l = 14.0\ cm = 0.14 \ m`

Since the test tube is closed at on end the frequency is mathematically represented as

`f = (v_s)/( 4 l )`

=>
`f = (344)/( 4 * 0.14 )`

=>
`f = 614.3 \ Hz`

From the part B the column of the test tube is half filled with water so the frequency becomes

`f_h = (v_s)/( 2 l )`

`f_h = (344)/( 2 * 0.14)`

`f_h = 1229 \ Hz`