Chapter 12, Problem 40P

To determine

Determine the beat frequency if middle C (262 Hz) and C (277 Hz) are played together and what if each played two octaves lower (each frequency reduced by a factor of 4).

Answer to Problem 40P

The beat frequency is 15 Hz can’t heat when played octaves it will become 3.75 Hz. Can be heard by the human.

Explanation of Solution

Given:

Frequency ( f₁ )  = 262 Hz.

Frequency ( f₂ )  = 277 Hz.

Determine the beat frequency ( f )=?

Formula used:

The beat frequency is determined by the difference in two frequencies.

Calculation:

The beat frequency for the given range of frequency can be determined by the difference between them.

277Hz - 262Hz = 15Hz.

But this may not be heard because the human ear can hear only 10 beats/s.

When each is played two octaves lower (each frequency reduced by a factor of 4). The beat frequency becomes,

  $\frac{15\text{ Hz}}{4}=3.75\text{ Hz}\text{.}$

The frequency 3.75 Hz can be heard by the human.

Conclusion:

The beat frequency can be determined by the difference of two frequencies but it cannot be heard by the human. When each is played two octaves the beat frequency becomes 3.75 Hz.