When a guitar is sounded with a 440 Hz tuning fork, a beat frequency of 5 Hz is heard. If the experiment is repeated with a tuning fork of 437 Hz, the beat frequency is 8 Hz. The string frequency (in Hz) is :-

Options

A. 445
B. 435
C. 429
D. 448

Explanation

To solve the problem step by step, we need to find the frequency of the guitar string based on the information given about the beat frequencies with two different tuning forks.

### Step 1: Define Variables
Let the frequency of the guitar string be denoted as \( V \).

### Step 2: Set Up the Equations
When the guitar is sounded with a 440 Hz tuning fork, a beat frequency of 5 Hz is heard. This can be expressed as:
\[ |V - 440| = 5 \]
This leads to two possible equations:
1. \( V - 440 = 5 \) (Equation 1)
2. \( 440 - V = 5 \) (Equation 2)

When the guitar is sounded with a 437 Hz tuning fork, a beat frequency of 8 Hz is heard. This can be expressed as:
\[ |V - 437| = 8 \]
This leads to two possible equations:
3. \( V - 437 = 8 \) (Equation 3)
4. \( 437 - V = 8 \) (Equation 4)

### Step 3: Solve the Equations
From Equation 1:
\[ V - 440 = 5 \]
\[ V = 445 \] (Solution from Equation 1)

From Equation 2:
\[ 440 - V = 5 \]
\[ V = 435 \] (Solution from Equation 2)

From Equation 3:
\[ V - 437 = 8 \]
\[ V = 445 \] (Solution from Equation 3)

From Equation 4:
\[ 437 - V = 8 \]
\[ V = 429 \] (Solution from Equation 4)

### Step 4: Analyze the Results
From the solutions obtained:
- From Equations 1 and 3, we have \( V = 445 \).
- From Equations 2 and 4, we have \( V = 435 \) and \( V = 429 \).

### Step 5: Use Consistency to Find the Correct Frequency
The consistent value for \( V \) from the first set of equations (1 and 3) is \( 445 \) Hz.

### Step 6: Final Answer
Thus, the frequency of the guitar string is:
\[ \boxed{445 \text{ Hz}} \]