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Step-by-Step Solution
Step 1: Understand the Concept of Beat Frequency
When two sources of sound have frequencies that are close to each other, they produce beats. The beat frequency, denoted by $f_{\text{beat}}$, is the absolute difference between the two frequencies.
Mathematically,
$
f_{\text{beat}} = |f_A - f_B|.
$
Here, $f_A$ and $f_B$ are the individual frequencies of the two strings A and B, respectively.
Step 2: Identify the Given Information
Strings A and B produce beats of frequency $6\,\text{Hz}$ when both are played together initially.
String A's frequency is given to be $530\,\text{Hz}$ after some adjustment (or from the context). We consider that $f_A > f_B$.
We need to find the original frequency of string B.
Step 3: Apply the Beat Frequency Formula
Since the beats produced are $6\,\text{Hz}$ originally and $f_A > f_B$, we use:
$
f_{\text{beat}} = f_A - f_B.
$
Given $f_{\text{beat}} = 6\,\text{Hz}$ and $f_A = 530\,\text{Hz}$, we substitute these into the equation:
$
6 = 530 - f_B.
$
Step 4: Solve for the Unknown Frequency of B
Rearranging the above equation, we get:
$
f_B = 530 - 6 = 524\,\text{Hz}.
$
This value, $524\,\text{Hz}$, is the original frequency of string B.
Final Answer
The original frequency of string B is $524\,\text{Hz}$.
