The disc of a siren revolves 600 times in one minute and it is in unison with a tuning fork of frequency 480 Hz. The number of holes in the disc is

Options

A. 24
B. 38
C. 48
D. 56

Answer

To solve the problem, we need to find the number of holes in the disc of the siren based on the given information. Here’s a step-by-step solution:

### Step 1: Determine the frequency of the disc
The disc revolves 600 times in one minute. To find the frequency in hertz (Hz), we convert revolutions per minute (rpm) to revolutions per second (rps):

\[ \text{Frequency of the disc} = \frac{600 \text{ revolutions}}{60 \text{ seconds}} = 10 \text{ Hz} \]

### Step 2: Relate the frequency of the siren to the number of holes
Let \( n \) be the number of holes in the disc. Since the disc is revolving and each hole passes a point in the siren, the frequency of the sound produced by the siren is given by:

\[ \text{Frequency of the siren} = n \times \text{Frequency of the disc} \]

Substituting the frequency of the disc we found:

\[ \text{Frequency of the siren} = n \times 10 \text{ Hz} \]

### Step 3: Set the frequency of the siren equal to the tuning fork frequency
We know that the frequency of the siren is in unison with a tuning fork of frequency 480 Hz. Therefore, we can set up the equation:

\[ n \times 10 = 480 \]

### Step 4: Solve for \( n \)
To find the number of holes \( n \), we rearrange the equation:

\[ n = \frac{480}{10} = 48 \]

### Conclusion
Thus, the number of holes in the disc is \( n = 48 \).

### Final Answer
The number of holes in the disc is **48**.

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