The equation of a wave travelling in a string can be written as `y = 3 cos pi (10t-x)`. Its wavelength is

Options

A. 100 cm
B. 2 cm
C. 5 cm
D. none of the above

Explanation

To find the wavelength of the wave described by the equation \( y = 3 \cos(\pi(10t - x)) \), we can follow these steps:

### Step 1: Rewrite the wave equation
The given wave equation is:
\[ y = 3 \cos(\pi(10t - x)) \]
We can rewrite this as:
\[ y = 3 \cos(\pi \cdot 10t - \pi x) \]

### Step 2: Identify the angular frequency and wave number
In the standard form of a wave equation, \( y = A \cos(\omega t - kx) \), we can identify:
- \( \omega = \pi \cdot 10 \)
- \( k = \pi \)

### Step 3: Calculate the wave number
From the wave number \( k \), we know the relationship:
\[ k = \frac{2\pi}{\lambda} \]
Given that \( k = \pi \), we can set up the equation:
\[ \pi = \frac{2\pi}{\lambda} \]

### Step 4: Solve for the wavelength \( \lambda \)
To find \( \lambda \), we can rearrange the equation:
\[ \lambda = \frac{2\pi}{\pi} \]
This simplifies to:
\[ \lambda = 2 \]

### Step 5: State the units
Since the problem does not specify units, we will assume the wavelength is in centimeters, thus:
\[ \lambda = 2 \text{ cm} \]

### Final Answer
The wavelength of the wave is \( 2 \text{ cm} \).

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