These 255.75 Hz and 256.25 Hz sounds can be thought of as a sum of two waves with frequencies.
Answer: Option A
Explanation:
To solve this, it is necessary to take into account the concepts related to frequency and period, and how they are related to each other.
Let frequency of beat = f
The relationship that defines both agreements is given by the equation,
[tex]f=\frac{1}{T}[/tex]
Then the frequency for the previous period given (2sec) is
[tex]f=\frac{1}{2}=0.5[/tex]
The beat frequency of two frequencies is equal to the difference between the two frequencies, then
[tex]f=\left|f_{1}-f_{2}\right|[/tex]
[tex]f=|255.75-256.25|=0.5 H z[/tex]
Hence, Option A is correct.
Similarly we can check like these for other options too as below,
For option B, [tex]f=|255.5-256.5|=1 Hz[/tex].
For Option C, [tex]f=|255-257|=2 H z[/tex]
For Option D, [tex]f=|254-258|=4 H z[/tex]
For Option E, [tex]f=|256-2|=254 H z[/tex]
Therefore, the sum of the frequencies in the sound wave would be 256.25Hz and 255.75Hz.
