Question

In: Physics

You blow across the open mouth of an empty test tube and producethe fundamental standing wave...

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

Expert Solution

Concepts and reason

The concept used to solve this problem is fundamental frequency.

Use equation of fundamental frequency to find the fundamental frequencies of the standing wave in the test tube.

Fundamentals

The expression for the wavelength of the fundamental harmonic for a tube with one end open and other end closed is as follows:

Here, is the wavelength and is the length of the tube.

Wavelength is also expressed as

Here, is the speed of the wave and is the fundamental frequency.

(a)

The fundamental frequency of the standing wave is,

Wavelength of the fundamental harmonic for a test tube is,

Substitute as and as .

(b)

The fundamental frequency of the standing wave is,

Wavelength of the fundamental harmonic for a test tube is,

Since the test tube is half filled with water, length is equal to,

Substitute as and as

Ans: Part a

Thus, the frequency of the standing wave is

Part b

Thus, the frequency of the standing wave is

genius_generous answered 2 years ago

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