Question

Two tuning forks produce frequencies \( 256 \text{ Hz} \) and \( 260 \text{ Hz} \). Number of beats per second is:

• A. \( 2 \)
• B. \( 4 \)
• C. \( 6 \)
• D. \( 8 \)

Hint:

To remember beats intuitively, think of it as a physical mismatch pattern. For a human ear to distinctly distinguish and count beats, the frequency difference should ideally be less than \(10 \text{ Hz}\) due to the physiological phenomenon of persistence of hearing!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The phenomenon of "beats" occurs when two sound waves of slightly different frequencies travel in the same direction and superimpose.
Because the waves are not exactly the same frequency, they alternate between constructive interference (where they add up to be loud, called 'waxing') and destructive interference (where they cancel out to be quiet, called 'waning').
The observer hears a single tone that pulsates in volume. The frequency of these pulses is what we call the "beat frequency."
Key Formula or Approach:
The beat frequency (\(f_b\)), or the number of beats heard per second, is simply the absolute difference between the frequencies of the two interfering sources.
\[ f_{beat} = |f_1 - f_2| \]
Step 2: Detailed Explanation:
We are given two tuning forks with frequencies:
Fork 1: \(f_1 = 256\) Hz.
Fork 2: \(f_2 = 260\) Hz.
To find the number of beats per second, we subtract the lower frequency from the higher frequency:
\[ \text{Beats per second} = 260 - 256 \]
\[ \text{Beats per second} = 4 \]
This means that in one second, the sound intensity will reach its maximum level four times.
Physically, this happens because the two waves come back into phase with each other exactly 4 times every second.
Step 3: Final Answer:
The number of beats per second is 4. This corresponds perfectly with option (B).