Question

A note produces 4 beats/s with a tuning fork of frequency \(510\,\text{Hz}\) and 6 beats/s with a fork of frequency \(512\,\text{Hz}\). The frequency of the note is

• A. \(506\,\text{Hz}\)
• B. \(514\,\text{Hz}\)
• C. \(518\,\text{Hz}\)
• D. \(510\,\text{Hz}\)

Hint:

When two beat conditions are given, choose the common frequency satisfying both.

Answer 1

The Correct Option is A

Step 1: Use beat frequency relation.
Beat frequency is given by:
\[ |f - f_0| \]
Step 2: Apply condition with first tuning fork.
\[ |f - 510| = 4 \Rightarrow f = 514 \text{ or } 506 \]
Step 3: Apply condition with second tuning fork.
\[ |f - 512| = 6 \Rightarrow f = 518 \text{ or } 506 \]
Step 4: Common value.
The common frequency satisfying both conditions is:
\[ f = 506\,\text{Hz} \]
Step 5: Conclusion.
The frequency of the note is \(506\,\text{Hz}\).