A plane wave is represented by
`x=1.2 sin (3 14 t + 12.56 y)`
Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has wavelength

Answer

To find the wavelength of the given plane wave represented by the equation \( x = 1.2 \sin(3140 t + 12.56 y) \), we can follow these steps:

### Step 1: Identify the wave equation format
The standard form of a wave equation is:
\[ x = A \sin(\omega t + k y) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

### Step 2: Compare the given equation with the standard form
From the given equation \( x = 1.2 \sin(3140 t + 12.56 y) \), we can identify:
- \( \omega = 3140 \) (angular frequency)
- \( k = 12.56 \) (wave number)

### Step 3: Relate wave number to wavelength
The wave number \( k \) is related to the wavelength \( \lambda \) by the formula:
\[ k = \frac{2\pi}{\lambda} \]

### Step 4: Solve for wavelength
Substituting the value of \( k \):
\[ 12.56 = \frac{2\pi}{\lambda} \]
To find \( \lambda \), rearranging the equation gives:
\[ \lambda = \frac{2\pi}{12.56} \]

### Step 5: Calculate the wavelength
Using \( \pi \approx 3.14 \):
\[ \lambda = \frac{2 \times 3.14}{12.56} \]
Calculating this:
\[ \lambda = \frac{6.28}{12.56} = 0.5 \text{ meters} \]

### Final Answer
The wavelength \( \lambda \) of the wave is:
\[ \lambda = 0.5 \text{ meters} \]

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