Question

You hear a sound with a frequency of 256 Hz. The amplitude of the sound increases and decreases periodically: It takes 2 seconds for the sound to go from loud to soft and back to loud. This sound can be thought of as a sum of two waves with frequencies Group of answer choices
255.75 Hz and 256.25 Hz.
255.5 Hz and 256.5 Hz.
255 Hz and 257 Hz.
254 Hz and 258 Hz.
256 Hz and 2 Hz.

Answer 1

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,

                $f=\frac{1}{T}$

Then the frequency for the previous period given (2sec) is

               $f=\frac{1}{2}=0.5$

The beat frequency of two frequencies is equal to the difference between the two frequencies, then

               $f=\left|f_{1}-f_{2}\right|$

               $f=|255.75-256.25|=0.5 H z$

Hence, Option A is correct.

Similarly we can check like these for other options too as below,

For option B, $f=|255.5-256.5|=1 Hz$.

For Option C, $f=|255-257|=2 H z$

For Option D, $f=|254-258|=4 H z$

For Option E, $f=|256-2|=254 H z$

Therefore, the sum of the frequencies in the sound wave would be 256.25Hz and 255.75Hz.