Question:
When a tuning fork of frequency 256 Hz is sounded together with unknown tuning fork, 4 beats are heard in one second. The frequency of the unknown tuning fork can be
When a tuning fork of frequency 256 Hz is sounded together with unknown tuning fork, 4 beats are heard in one second. The frequency of the unknown tuning fork can be
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Always use the \(\pm\) sign for unknown frequency problems unless there is extra information (like "frequency increases on waxing" or "decreases on filing").
Updated On: Apr 29, 2026
- 260 Hz or 252 Hz
- 258 Hz or 256 Hz
- 250 Hz or 256 Hz
- 248 Hz or 255 Hz
- 257 Hz or 215 Hz
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Beats are produced when two sound waves of slightly different frequencies interfere. The beat frequency (\(n\)) is equal to the absolute difference between the two frequencies.
Step 2: Key Formula or Approach:
\[ n = |f_1 - f_2| \]
or \(f_2 = f_1 \pm n\).
Step 3: Detailed Explanation:
Given:
Known frequency \(f_1 = 256 \text{ Hz}\).
Beat frequency \(n = 4 \text{ beats per second}\).
The frequency of the unknown fork (\(f_2\)) can be either higher or lower than the known frequency by the value of the beat frequency.
Case 1 (Higher): \(f_2 = 256 + 4 = 260 \text{ Hz}\).
Case 2 (Lower): \(f_2 = 256 - 4 = 252 \text{ Hz}\).
Step 4: Final Answer:
The frequency can be 260 Hz or 252 Hz.
Beats are produced when two sound waves of slightly different frequencies interfere. The beat frequency (\(n\)) is equal to the absolute difference between the two frequencies.
Step 2: Key Formula or Approach:
\[ n = |f_1 - f_2| \]
or \(f_2 = f_1 \pm n\).
Step 3: Detailed Explanation:
Given:
Known frequency \(f_1 = 256 \text{ Hz}\).
Beat frequency \(n = 4 \text{ beats per second}\).
The frequency of the unknown fork (\(f_2\)) can be either higher or lower than the known frequency by the value of the beat frequency.
Case 1 (Higher): \(f_2 = 256 + 4 = 260 \text{ Hz}\).
Case 2 (Lower): \(f_2 = 256 - 4 = 252 \text{ Hz}\).
Step 4: Final Answer:
The frequency can be 260 Hz or 252 Hz.
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