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4. The longest pipe in a certain organ is 4.00 meters long. What are the frequencies of the fundamental and first two overtones the organ will produce if the pipe is (i) open at both ends; (ii) closed at one end? ii) Open at both ends: a) Sketch the first three resonances in the open pipe (see Fig. 16-41). n=1 n=2 n=3 b) Write down the equation(s) governing harmonics in an open pipe (Eq. 16-31 and 16-32) c) Calculate the fundamental frequency, assuming the speed of sound is 344 m/s. f₁ = Hz d) Calculate the next two frequencies by doubling and tripling. f₂ = Hz f; = Hz ii) Closed at one end: a) Sketch the first three resonances in the closed pipe (see Fig. 16-42). n=1 n = ? n= b) Write down the equation(s) governing harmonics in an closed pipe (Eq. 16-33 and 16-34) c) Calculate the fundamental frequency, assuming the speed of sound is 344 m/s. f₁ = Hz

4. The longest pipe in a certain organ is 4.00 meters long. What are the frequencies of the fundamental and first two overtones the organ will produce if the pipe is (i) open at both ends; (ii) closed at one end? ii) Open at both ends: a) Sketch the first three resonances in the open pipe (see Fig. 16-41). n=1 n=2 n=3 b) Write down the equation(s) governing harmonics in an open pipe (Eq. 16-31 and 16-32) c) Calculate the fundamental frequency, assuming the speed of sound is 344 m/s. f₁ = Hz d) Calculate the next two frequencies by doubling and tripling. f₂ = Hz f; = Hz ii) Closed at one end: a) Sketch the first three resonances in the closed pipe (see Fig. 16-42). n=1 n = ? n= b) Write down the equation(s) governing harmonics in an closed pipe (Eq. 16-33 and 16-34) c) Calculate the fundamental frequency, assuming the speed of sound is 344 m/s. f₁ = Hz

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Can you help me with number 4 please
## Frequencies of Harmonics in Organ Pipes ### Problem Statement The longest pipe in a certain organ is 4.00 meters long. Determine the frequencies of the fundamental and first two overtones the organ will produce if the pipe is: i) Open at both ends ii) Closed at one end ### Part (i): Open at Both Ends #### a) Sketch the First Three Resonances in the Open Pipe (see Fig. 16-41) - \(n = 1\) - \(n = 2\) - \(n = 3\) (Here, students are expected to sketch the corresponding resonance patterns for n=1, n=2, and n=3.) #### b) Write Down the Equation(s) Governing Harmonics in an Open Pipe (Eq. 16-31 and 16-32) #### c) Calculate the Fundamental Frequency, Assuming the Speed of Sound is 344 m/s \[ f_1 = \, \_\_\_\_\_\_ \, \text{Hz} \] #### d) Calculate the Next Two Frequencies by Doubling and Tripling \[ f_2 = \, \_\_\_\_\_\_ \, \text{Hz} \] \[ f_3 = \, \_\_\_\_\_\_ \, \text{Hz} \] ### Part (ii): Closed at One End #### a) Sketch the First Three Resonances in the Closed Pipe (see Fig. 16-42) - \(n = 1\) - \(n = \, ? \) - \(n = \, ? \) (Here, students are expected to sketch the corresponding resonance patterns for n=1 and the next two values of n.) #### b) Write Down the Equation(s) Governing Harmonics in a Closed Pipe (Eq. 16-33 and 16-34) #### c) Calculate the Fundamental Frequency, Assuming the Speed of Sound is 344 m/s \[ f_1 = \, \_\_\_\_\_\_ \, \text{Hz} \] --- ### Explanation of Diagrams - **For open pipes**: These diagrams should represent the standing wave patterns for the first three harmonics. Each successive harmonic will include one additional antinode (point of maximum amplitude) and node (point of minimum amplitude). - **For closed pipes**: These diagrams should represent the standing wave patterns
Transcribed Image Text:## Frequencies of Harmonics in Organ Pipes ### Problem Statement The longest pipe in a certain organ is 4.00 meters long. Determine the frequencies of the fundamental and first two overtones the organ will produce if the pipe is: i) Open at both ends ii) Closed at one end ### Part (i): Open at Both Ends #### a) Sketch the First Three Resonances in the Open Pipe (see Fig. 16-41) - \(n = 1\) - \(n = 2\) - \(n = 3\) (Here, students are expected to sketch the corresponding resonance patterns for n=1, n=2, and n=3.) #### b) Write Down the Equation(s) Governing Harmonics in an Open Pipe (Eq. 16-31 and 16-32) #### c) Calculate the Fundamental Frequency, Assuming the Speed of Sound is 344 m/s \[ f_1 = \, \_\_\_\_\_\_ \, \text{Hz} \] #### d) Calculate the Next Two Frequencies by Doubling and Tripling \[ f_2 = \, \_\_\_\_\_\_ \, \text{Hz} \] \[ f_3 = \, \_\_\_\_\_\_ \, \text{Hz} \] ### Part (ii): Closed at One End #### a) Sketch the First Three Resonances in the Closed Pipe (see Fig. 16-42) - \(n = 1\) - \(n = \, ? \) - \(n = \, ? \) (Here, students are expected to sketch the corresponding resonance patterns for n=1 and the next two values of n.) #### b) Write Down the Equation(s) Governing Harmonics in a Closed Pipe (Eq. 16-33 and 16-34) #### c) Calculate the Fundamental Frequency, Assuming the Speed of Sound is 344 m/s \[ f_1 = \, \_\_\_\_\_\_ \, \text{Hz} \] --- ### Explanation of Diagrams - **For open pipes**: These diagrams should represent the standing wave patterns for the first three harmonics. Each successive harmonic will include one additional antinode (point of maximum amplitude) and node (point of minimum amplitude). - **For closed pipes**: These diagrams should represent the standing wave patterns
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