Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Two organ pipes, open at one end but closed at the other, are each 1.03 m long. One is now lengthened by 1.50 cm. Find the beat frequency they produce when playing together in their fundamental.

Sagot :

okpalawalter8

Answer:

[tex]f=1.297Hz[/tex]

Explanation:

From the question we are told that:

Initial pipe length [tex]L_1=1.03m[/tex]

Final pipe length [tex]L_2=1.03+(1.50*10^-2)[/tex]

                             [tex]L_2=1.045m[/tex]

Generally the equation for Frequency f is mathematically given by

 [tex]F=\frac{v}{\lambda}[/tex]

Where

 [tex]\lambda=4L[/tex]

And

V=speed of sound in air

 [tex]v=343m/s[/tex]

Therefore

 [tex]f=\frac{v}{4}{\frac{1}{L_1}-\frac{1}{L_2}}[/tex]

 [tex]f=\frac{343}{4}{\frac{1}{1.03}-\frac{1}{1.045}}[/tex]

 [tex]f=1.297Hz[/tex]

onyebuchinnaji

The beat frequency they produce when playing together in their fundamental is 1.2 Hz.

The given parameters;

  • initial pipe length, Lā‚ = 1.03 m
  • final pipe length, Lā‚‚ = 1.03 m + 1.5 cm = 1.03 m + 0.015 m = 1.045 m

The frequency of wave is calculated as follows;

[tex]v = f \lambda \\\\f = \frac{v}{\lambda }[/tex]

The fundamental frequency of closed pipe is calculated as follows;

[tex]L= \frac{\lambda}{4} \\\\\lambda = 4L\\\\f = \frac{v}{4L}[/tex]

The beat frequency is calculated as follows;

[tex]f_0 - f_1 = \frac{v}{4L_0} - \frac{v}{4L_1} \\\\f_0 - f_1 = \frac{v}{4} (\frac{1}{L_0} - \frac{1}{L_1} )\\\\f_0 - f_1 = \frac{343}{4} (\frac{1}{1.03} - \frac{1}{1.045} )\\\\f_0 - f_1 = 1.2 \ Hz[/tex]

Thus, the beat frequency they produce when playing together in their fundamental is 1.2 Hz.

Learn more here:https://brainly.com/question/23432691

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.