Musical Acoustics, Combining frequencies of two instruments

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SUMMARY

The discussion centers on estimating the operating frequency of a brand X dog whistle that, when combined with another whistle operating at 21.5 kHz, produces a beat frequency of 5000 Hz. The correct approach involves using the formula for beat frequencies, which states that the beat frequency equals the absolute difference between the two frequencies. Thus, the equation should be set as |21.5 kHz - X kHz| = 5 kHz, leading to two possible solutions for X: 16.5 kHz or 26.5 kHz.

PREREQUISITES
  • Understanding of beat frequencies in acoustics
  • Familiarity with basic algebraic manipulation
  • Knowledge of frequency measurement in kHz
  • Concept of sound wave interference
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  • Learn about sound wave interference and its applications
  • Explore the mathematical relationships between frequencies in acoustics
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mhmil
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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.
 
Physics news on Phys.org
Beats are the difference of two frequencies.
Fw2 = Fw1 + or - F(beat).
 
Thanks!
 

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