Question:
A source of frequency \( \nu \) gives 6 beats/second when sounded with a source of frequency 200 Hz. The second Harmonic of frequency \( 2\nu \) of the source gives 8 beats/second when sounded with a source of frequency 420 Hz. The value of \( \nu \) is
A source of frequency \( \nu \) gives 6 beats/second when sounded with a source of frequency 200 Hz. The second Harmonic of frequency \( 2\nu \) of the source gives 8 beats/second when sounded with a source of frequency 420 Hz. The value of \( \nu \) is
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Always solve beat frequency equations carefully and check for common values when multiple conditions are given.
Updated On: Apr 23, 2026
- 205 Hz
- 206 Hz
- 195 Hz
- 210 Hz
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
A source of frequency \( \nu \) produces 6 beats per second with a 200 Hz source.
Its second harmonic \( 2\nu \) produces 8 beats per second with a 420 Hz source.
Step 2: Key Formula or Approach:
Number of beats per second: \[ \text{Beats} = |f_1 - f_2| \] Step 3: Detailed Explanation:
From the first condition: \[ |\nu - 200| = 6 \] \[ \nu = 200 \pm 6 = 206 \text{ Hz or } 194 \text{ Hz} \] From the second condition: \[ |2\nu - 420| = 8 \] \[ 2\nu = 420 \pm 8 = 428 \text{ or } 412 \] \[ \nu = 214 \text{ Hz or } 206 \text{ Hz} \] Now, the common value from both conditions is: \[ \nu = 206 \text{ Hz} \] Step 4: Final Answer:
\[ \boxed{206 \text{ Hz}} \]
A source of frequency \( \nu \) produces 6 beats per second with a 200 Hz source.
Its second harmonic \( 2\nu \) produces 8 beats per second with a 420 Hz source.
Step 2: Key Formula or Approach:
Number of beats per second: \[ \text{Beats} = |f_1 - f_2| \] Step 3: Detailed Explanation:
From the first condition: \[ |\nu - 200| = 6 \] \[ \nu = 200 \pm 6 = 206 \text{ Hz or } 194 \text{ Hz} \] From the second condition: \[ |2\nu - 420| = 8 \] \[ 2\nu = 420 \pm 8 = 428 \text{ or } 412 \] \[ \nu = 214 \text{ Hz or } 206 \text{ Hz} \] Now, the common value from both conditions is: \[ \nu = 206 \text{ Hz} \] Step 4: Final Answer:
\[ \boxed{206 \text{ Hz}} \]
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