The equation of a plane progressive wave is given by `y=5cos(200t-(pi)/(150)x)` where `x` and `y` in cm and `t` is in second. The wavelength of the wave is

Answer

To find the wavelength of the wave given by the equation \( y = 5 \cos(200t - \frac{\pi}{150}x) \), we will follow these steps:

### Step 1: Identify the wave equation format
The general form of a plane progressive wave is given by:
\[ y = A \cos(\omega t - kx) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number.

### Step 2: Compare with the given equation
From the given equation \( y = 5 \cos(200t - \frac{\pi}{150}x) \), we can identify:
- \( \omega = 200 \) (in radians per second),
- \( k = \frac{\pi}{150} \) (in radians per centimeter).

### 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: Rearrange the formula to find wavelength
We can rearrange this formula to solve for \( \lambda \):
\[ \lambda = \frac{2\pi}{k} \]

### Step 5: Substitute the value of \( k \)
Now substitute the value of \( k \) into the equation:
\[ \lambda = \frac{2\pi}{\frac{\pi}{150}} = 2\pi \cdot \frac{150}{\pi} \]

### Step 6: Simplify the expression
The \( \pi \) in the numerator and denominator cancels out:
\[ \lambda = 2 \cdot 150 = 300 \text{ cm} \]

### Final Answer
Thus, the wavelength of the wave is:
\[ \lambda = 300 \text{ cm} \]

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