If the sound waves produced by the tuning fork can be expressed as `y = 0.2 (cm) sin (kx - omega t)` , where `K = 2 pi//lambda` and `omega = 2 pi f (f = 512 Hz)`, maximum value of amplitude in a beat will be

Options

A. `0.4 cm`
B. `0.6 cm`
C. `0.8 cm`
D. `0.2 cm`

Explanation

To solve the problem step by step, we will analyze the given wave equation and determine the maximum amplitude of the beats produced by the superposition of two sound waves.

### Step 1: Understand the wave equation
The wave produced by the tuning fork is given by:
\[ y = 0.2 \, \text{cm} \, \sin(kx - \omega t) \]
Here, \( 0.2 \, \text{cm} \) is the amplitude of the wave.

### Step 2: Identify the amplitude of the wave
The amplitude of the wave is the coefficient in front of the sine function. Therefore, the amplitude \( A \) of the sound wave is:
\[ A = 0.2 \, \text{cm} \]

### Step 3: Determine the nature of beats
When two waves of slightly different frequencies interfere, they produce a phenomenon called beats. The amplitude of the resulting wave can vary between the sum and the difference of the individual amplitudes.

### Step 4: Calculate the maximum amplitude of the beats
If two waves with the same amplitude \( A \) interfere, the maximum amplitude of the resulting wave (the beat) can be calculated as:
\[ A_{\text{max}} = A_1 + A_2 \]
Since both waves have the same amplitude \( A = 0.2 \, \text{cm} \):
\[ A_{\text{max}} = 0.2 \, \text{cm} + 0.2 \, \text{cm} = 0.4 \, \text{cm} \]

### Step 5: Conclusion
Thus, the maximum value of the amplitude in a beat will be:
\[ \text{Maximum Amplitude} = 0.4 \, \text{cm} \]

### Final Answer
The maximum value of amplitude in a beat will be **0.4 cm**.

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