Musical Acoustics, Combining frequencies of two instruments

In summary, the conversation discusses the estimation of the operating frequency of a dog whistle (brand X) based on its shrill whine when played simultaneously with another whistle at 21.5 kHz. The equation Fw2 = Fw1 + or - F(beat) is mentioned, where Fw2 represents the frequency of brand X, Fw1 represents the frequency of the other whistle, and F(beat) represents the difference of the two frequencies. The attempt at a solution involved setting up the equation 21.5 kHz + X kHz = 5 kHz and solving for X, resulting in a negative value of -16.5 kHz. However, this does not make sense and is not accepted as an answer by the
  • #1
mhmil
8
0

Homework Statement



A certain dog whistle operates at 21.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X. (Find your answer in kHz, not Hz, but do not enter units. So if you think the answer is 2000 Hz = 2.0 kHz, enter 2.0 )


Homework Equations



Unsure.


The Attempt at a Solution



I've tried 21.5khz + X khz = 5khz and solved for X, -16.5 khz. This doesn't make any sense, as how could it be negative? My homework doesn't accept this as an answer either (obviously.)

Any help would be greatly appreciated.
 
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  • #2
Beats are the difference of two frequencies.
Fw2 = Fw1 + or - F(beat).
 
  • #3
Thanks!
 

1. What is musical acoustics?

Musical acoustics is the study of how sound is produced, transmitted, and perceived in relation to music. It involves understanding the physical properties of sound waves and how they are influenced by musical instruments and the human ear.

2. How do two instruments combine their frequencies to create harmony?

When two instruments play together, their sound waves interact and combine to create a new sound. This is known as interference, and it can result in either consonance (harmony) or dissonance (clashing sounds). The frequencies of the two instruments must be in a certain ratio to create a pleasing harmony.

3. What is the difference between consonance and dissonance?

Consonance refers to the pleasant, harmonious sound created when two or more frequencies combine in a simple ratio, such as 2:1 or 3:2. Dissonance, on the other hand, refers to the harsh or unpleasant sound created when frequencies combine in complex ratios, such as 17:12 or 5:4.

4. How do musicians use the principles of musical acoustics in their performances?

Musicians use their understanding of musical acoustics to create harmony and balance in their performances. They may adjust the frequencies of their instruments or use techniques such as vibrato to enhance the sound. They also use the principles of acoustics to choose the best concert venues and to amplify their sound for larger audiences.

5. Can musical acoustics be applied to other areas besides traditional instruments?

Yes, musical acoustics can be applied to any sound-producing object or system. This includes electronic instruments, vocal techniques, and even environmental sounds. By understanding the principles of acoustics, we can better appreciate and manipulate the sounds around us in various contexts.

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