The frequency of beats produced when two tunning forks of frequencies 258Hz and 270Hz are sounded close to each other

Analyze the question: Two tuning forks with different frequencies are sounded together. We need the beat frequency.

Concept: Beats are produced when two sound waves of slightly different frequencies interfere. The beat frequency is the absolute difference between the two frequencies:

f_beat = |f₁ − f₂|

Solution:

• f₁ = 270 Hz
• f₂ = 258 Hz

f_beat = 270 − 258 = 12 Hz

Checking the other options:

• A (6 Hz): this is half the difference, which is a wrong use of the formula.
• B (264 Hz): this is the average of the two frequencies, (258 + 270)/2. It is the pitch you actually hear, not the beat frequency.
• C (528 Hz): this is the sum of the two frequencies, which is not what beats depend on.
• D (12 Hz): this is the difference, which is correct.

Tip: Remember "beats = take away". Subtract the frequencies. The average (264 Hz) is the tone you hear, and the difference (12 Hz) is how many times per second the loudness rises and falls. JAMB often puts the sum or average among the options as traps.