A wave is represented by the equetion
`y=7 sin(7pi t-0.04pix+(pi)/(3))`
x is in metres and t is in seconds. The speed of the wave is

Options

A. `175 m//s`
B. `49pi m//s`
C. `49//pi m//s`
D. `0.28 pi m//s`

Explanation

To find the speed of the wave represented by the equation

\[ y = 7 \sin(7\pi t - 0.04\pi x + \frac{\pi}{3}) \]

we will follow these steps:

### Step 1: Identify the wave equation components
The general form of a wave equation is

\[ y = A \sin(\omega t - kx + \phi) \]

where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number,
- \( \phi \) is the phase constant.

From the given equation, we can identify:
- \( A = 7 \)
- \( \omega = 7\pi \)
- \( k = 0.04\pi \)
- \( \phi = \frac{\pi}{3} \)

### Step 2: Calculate the wave speed
The speed of the wave \( v \) can be calculated using the formula:

\[ v = \frac{\omega}{k} \]

### Step 3: Substitute the values of \( \omega \) and \( k \)
Now, substituting the values we identified:

\[ v = \frac{7\pi}{0.04\pi} \]

### Step 4: Simplify the expression
The \( \pi \) in the numerator and denominator cancels out:

\[ v = \frac{7}{0.04} \]

Calculating \( \frac{7}{0.04} \):

\[ v = 7 \times \frac{1}{0.04} = 7 \times 25 = 175 \, \text{m/s} \]

### Final Answer
Thus, the speed of the wave is

\[ v = 175 \, \text{m/s} \]

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