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
The mystery whistle has a frequency that is 9200 Hz or 9.2 kHz from the other, which means is at 23.5 ±9.2 kHz, which means the two options are 32.7 kHz (above human hearing - Ultrasound) or 14.3 kHz (below human and dog hearing - Infrasound) Then the other whistle must be the higher frequency of 32.7 kHz.
It would have to be 32.7 kHz because humans can hear 14.3 kHz
To estimate the operating frequency of brand X dog whistle, we can use the phenomenon of Beat Frequency.
The beat frequency is the absolute difference in frequency between two waves that are superimposed. In this case, when the two dog whistles are played simultaneously, a shrill whine of frequency 9200 Hz occurs.
Given that the first dog whistle operates at 23.5 kHz (23,500 Hz), we can calculate the beat frequency by subtracting the known frequency from the observed frequency:
Beat frequency = Observed frequency - Known frequency
Beat frequency = 9200 Hz - 23,500 Hz
Beat frequency = -14,300 Hz
Since the beat frequency is negative, it suggests that the frequency of brand X dog whistle is lower than the known frequency. To estimate the operating frequency of brand X, we will add the absolute value of the beat frequency to the known frequency:
Operating frequency of brand X = Known frequency + |Beat frequency|
Operating frequency of brand X = 23,500 Hz + |-14,300 Hz|
Operating frequency of brand X = 23,500 Hz + 14,300 Hz
Operating frequency of brand X ≈ 37,800 Hz
Therefore, the estimated operating frequency of brand X dog whistle is approximately 37,800 Hz.
To estimate the operating frequency of brand X, we can use the concept of beat frequencies. When two sound waves of slightly different frequencies are played together, they produce a beat frequency equal to the difference between their frequencies.
In this case, the beat frequency is given as 9200 Hz. Since the human hearing range is typically up to 20 kHz (20,000 Hz), we know that 23.5 kHz is beyond the range of human hearing.
Now, let's use the formula for beat frequency:
Beat Frequency = |Frequency 1 - Frequency 2|
We know that Frequency 1 is 23.5 kHz (23,500 Hz) and the Beat Frequency is 9200 Hz. Let's put this formula into equation form:
9200 Hz = |23,500 Hz - Frequency 2|
To find Frequency 2 (the operating frequency of brand X), we need to isolate the unknown frequency. Rearranging the equation, we have:
Frequency 2 = 23,500 Hz - 9200 Hz
Frequency 2 = 14,300 Hz
Therefore, the estimated operating frequency of brand X is 14,300 Hz.