A certain dog whistle operates at 23.5 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 9200 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.
____Hz
23.5 + 9.2 = 32.7 k Hz = 32700 Hz
To estimate the operating frequency of brand X, we can use the concept of beats.
When two sound waves with slightly different frequencies are played simultaneously, they create a phenomenon called beats. Beats occur due to the interference between the two sound waves. This interference results in a periodic variation in the amplitude of the resulting waveform, causing a perceived "whine" or intensity variation.
In this case, we know that the dog whistle operates at 23.5 kHz (23,500 Hz). When played simultaneously with brand X, it creates a shrill whine of frequency 9200 Hz.
To estimate the operating frequency of brand X, we can calculate the difference between the frequency of the whine and the known frequency (23.5 kHz).
Difference in frequency = 23,500 Hz - 9200 Hz
Therefore, the operating frequency of brand X can be estimated as:
Operating frequency of brand X = 23,500 Hz - 9200 Hz = 14,300 Hz
Hence, the estimated operating frequency of brand X is 14,300 Hz.