The displacement at a pont due to two waves are given by `y_(1)=2sin(50pit) and y_(2)=3sin(58pit)` number of beats produced per second is

Options

A. 8
B. 4
C. 58
D. 50

Answer

To solve the problem of finding the number of beats produced per second by the two waves, we will follow these steps:

### Step 1: Identify the angular frequencies
The displacement equations of the two waves are given as:
- \( y_1 = 2 \sin(50 \pi t) \)
- \( y_2 = 3 \sin(58 \pi t) \)

From these equations, we can identify the angular frequencies (\( \omega_1 \) and \( \omega_2 \)):
- For wave 1: \( \omega_1 = 50 \pi \)
- For wave 2: \( \omega_2 = 58 \pi \)

### Step 2: Calculate the frequencies
The frequency (\( f \)) is related to the angular frequency (\( \omega \)) by the formula:
\[ f = \frac{\omega}{2\pi} \]

Now, we can calculate the frequencies for both waves:
- For wave 1:
\[ f_1 = \frac{\omega_1}{2\pi} = \frac{50 \pi}{2\pi} = 25 \text{ Hz} \]
- For wave 2:
\[ f_2 = \frac{\omega_2}{2\pi} = \frac{58 \pi}{2\pi} = 29 \text{ Hz} \]

### Step 3: Calculate the beat frequency
The beat frequency (\( f_b \)) is given by the absolute difference between the two frequencies:
\[ f_b = |f_2 - f_1| = |29 - 25| = 4 \text{ Hz} \]

### Conclusion
The number of beats produced per second is \( 4 \) beats per second.

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