In the wave equation,
`y = Asin(2pi)((x)/(a) - (t)/(b))`

Options

A. speed of wave is `a//b`
B. speed of wave is `b//a`
C. wavelength of wave is `a`
D. Time period of wave is `b`

Explanation

To solve the given wave equation \( y = A \sin\left(2\pi\left(\frac{x}{a} - \frac{t}{b}\right)\right) \), we need to find the speed of the wave, the wavelength, and the time period.

### Step 1: Identify the coefficients
The wave equation can be rewritten as:
\[ y = A \sin\left(2\pi \frac{x}{a} - 2\pi \frac{t}{b}\right) \]
From this form, we can identify:
- The coefficient of \( x \) is \( k = \frac{2\pi}{a} \)
- The coefficient of \( t \) is \( \omega = \frac{2\pi}{b} \)

### Step 2: Calculate the speed of the wave
The speed of the wave \( v \) is given by the formula:
\[ v = \frac{\omega}{k} \]
Substituting the values of \( \omega \) and \( k \):
\[ v = \frac{\frac{2\pi}{b}}{\frac{2\pi}{a}} = \frac{a}{b} \]

### Step 3: Calculate the wavelength
The wavelength \( \lambda \) is related to the wave number \( k \) by the formula:
\[ k = \frac{2\pi}{\lambda} \]
From our earlier identification, we have \( k = \frac{2\pi}{a} \). Setting these equal gives:
\[ \frac{2\pi}{\lambda} = \frac{2\pi}{a} \]
Thus, solving for \( \lambda \):
\[ \lambda = a \]

### Step 4: Calculate the time period
The time period \( T \) is related to the angular frequency \( \omega \) by the formula:
\[ \omega = \frac{2\pi}{T} \]
From our identification, we have \( \omega = \frac{2\pi}{b} \). Setting these equal gives:
\[ \frac{2\pi}{T} = \frac{2\pi}{b} \]
Thus, solving for \( T \):
\[ T = b \]

### Summary of Results
- Speed of the wave \( v = \frac{a}{b} \)
- Wavelength \( \lambda = a \)
- Time period \( T = b \)