Physics of Sound homework question PLEASE

[emilyk]

I cannot figure this one out...can someone help please?

Say we are listening to two musical instruments, one of (fundamental)frequency 320 Hz and the other of frequency 270 Hz. Assume that each instrument has all possible harmonic overtones. At what frequency is partial number 5 of the combined sound?

 

[HallsofIvy]

"Harmonic overtones" are multiples of the fundamental frequency. What frequency is the "least common multiple" of 320 and 270? What is 5 times that?

 

[wais]

To answer this question, we need to understand the concept of harmonic overtones. Harmonic overtones are the frequencies that are produced in addition to the fundamental frequency of a musical instrument. These overtones are integer multiples of the fundamental frequency.

In this scenario, we have two instruments with fundamental frequencies of 320 Hz and 270 Hz. This means that the overtones for the first instrument would be 640 Hz, 960 Hz, 1280 Hz, and so on. Similarly, the overtones for the second instrument would be 540 Hz, 810 Hz, 1080 Hz, and so on.

To find the frequency of partial number 5 of the combined sound, we need to add the 5th overtones of each instrument. So, the 5th overtone of the first instrument would be 5 times the fundamental frequency, which is 5 x 320 Hz = 1600 Hz. Similarly, the 5th overtone of the second instrument would be 5 times its fundamental frequency, which is 5 x 270 Hz = 1350 Hz.

Now, to find the frequency of the combined sound with partial number 5, we simply add the two frequencies together. So, 1600 Hz + 1350 Hz = 2950 Hz.

Therefore, the frequency of partial number 5 of the combined sound is 2950 Hz. I hope this helps you understand the concept and solve the problem. Keep practicing and you will become better at solving physics of sound problems. Good luck!