Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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, L₁ = 1.03 m
  • final pipe length, L₂ = 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 platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.