Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

A tube is open only at one end. A certain harmonic produced by the tube has a frequency of 475 hz. The next higher harmonic has a frequency of 1425 hz. The speed of sound in air is 343 m/s

Sagot :

shubhamchouhanvrVT

The formula for the fundamental frequency for an open tube at one end is : F = nV/4L the integer n = 3 which describe the frequency 450 hertz and length of tube L = 0.6m approximately

What is frequency?

Frequency of the object is defined as the number of cycles attend in a second .

Given that a tube is open only at one end. And a certain harmonic produced by the tube has a frequency of 450 Hz. The next higher harmonic has a frequency of 750 Hz. The formula for the fundamental frequency for an open tube at one end is :

[tex]F = \dfrac{V}{4L}[/tex]

That is, 1st harmonic

[tex]\dfrac{V}{4L} = F[/tex]

2nd harmonic =

[tex]\dfrac{3V}{4L} = 3F[/tex]

3rd harmonic =

[tex]\dfrac{5V}{4L} = 5F[/tex]

The general formula can therefore be [tex]F =\dfrac{ nV}{4L}[/tex]

For the first harmonic in the question,

[tex]450 = \dfrac{343n}{4L}[/tex]

make 4L the subject of the formula

[tex]4L = \dfrac{343n}{450}[/tex]

The next higher harmonic will be

[tex]750 = \dfrac{343(n + 2)}{4L}[/tex]

make 4L the subject of the formula

[tex]4L = \dfrac{343(n + 2)}{ 750}[/tex]

Equate the two 4L

[tex]\dfrac{343n}{450} = \dfrac{343( n + 2)}{750}[/tex]

cross multiply

[tex]257250n = 154350( n + 2 )[/tex]

[tex]257250n = 154350n + 308700[/tex]

collect the likes term

[tex]257250n - 154350n = 308700[/tex]

[tex]102900n = 308700[/tex]

[tex]n =\dfrac{ 308700}{102900}[/tex]

n = 3

Given that the speed of sound in air is 343 m/s, The length of the tube can be calculate by using the same formula.

[tex]F = \dfrac{nV}{4L}[/tex]

[tex]450 = \dfrac{3(343)}{4L}[/tex]

[tex]4L = \dfrac{1029}{450}[/tex]

4L = 2.28

[tex]L = \dfrac{2.28}{4}[/tex]

L = 0.57 m

To know more about Frequency follow

brainly.com/question/11944036

#SPJ4

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.