When two organ pipes open at both ends sound a perfect fifth, such as two notes

Question

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes? a. 440, 880 and 1 320 Hz. b. 660, 1 320 and 1 980 Hz. c. 880, 1 320 and 1 760 Hz. d. 1320, 2 640 and 3 960 Hz. e. They have no overtones in common. ANS: D PTS: 2 DIF: Average When two organ pipes each closed at one end sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes:? a. 440, 880 and 1 320 Hz. b. 660, 1 320 and 1 980 Hz. c. 880, 1 320 and 1 760 Hz. d. 1320, 2 640 and 3 960 Hz. e. They have no overtones in common. ANS: E PTS: 3 DIF: Challenging Two organ pipes, a pipe of fundamental frequency 440 Hz, closed at one end, and a pipe of fundamental frequency 660 Hz, open at both ends, produce overtones. Which choice below correctly describes overtones present in both pipes? a. After the first overtone of each pipe, every second overtone of the first pipe matches every second overtone of the second pipe After the first overtone of each pipe, every second overtone of the first pipe matches every third overtone of the second pipe. After the first overtone of each pipe, every third overtone of the first pipe matches every second overtone of the second pipe After the first overtone of each pipe, every second overtone of the first pipe matches every fourth overtone of the second pipe After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe b. c. d. e. ANS: E PTS: 3 DIF: Challenging

Explanation / Answer

Overtones are integral multiples of characteristic frequency.
Concept of overtones: For the first overtone, the organ pipe vibrates at 2 times the fundamental frequency, for the second overtone, the organ pipe vibrates at 3 times the fundamental frequency and so on.

Checking from the options, the frequency of vibration should be a multiple of both 440 and 660 to be an overtone of both of them.

Now, 1320 Hz is the second overtone of the pipe with fundamental frequency 440 Hz and it is the first overtone of pipe with fundamental frequency 660 Hz.

Similarly, 2640Hz is the fifth overtone of the pipe with fundamental frequency 440 Hz and it is the third overtone of pipe with fundamental frequency 660 Hz.

Lastly, 3960 Hz is the eighth overtone of the pipe with fundamental frequency 440 Hz and it is the fifth overtone of pipe with fundamental frequency 660 Hz.

And hence, the answer is D.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.