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

Options

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

Explanation

To solve the given wave equation \( y = A \sin\left(\frac{2\pi}{A}(x - bt)\right) \), we need to find the speed of the wave and its wavelength. Let's break this down step by step.

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

### Step 2: Rewrite the given equation
The given equation is:
\[ y = A \sin\left(\frac{2\pi}{A}(x - bt)\right) \]
We can rewrite it in the standard form:
\[ y = A \sin\left(\frac{2\pi}{A}x - \frac{2\pi b}{A}t\right) \]

### Step 3: Identify \( k \) and \( \omega \)
From the rewritten equation:
- The coefficient of \( x \) is \( k = \frac{2\pi}{A} \)
- The coefficient of \( t \) is \( \omega = \frac{2\pi b}{A} \)

### Step 4: Calculate the speed of the wave
The speed of the wave \( v \) can be calculated using the formula:
\[ v = \frac{\omega}{k} \]
Substituting the values of \( \omega \) and \( k \):
\[ v = \frac{\frac{2\pi b}{A}}{\frac{2\pi}{A}} = b \]

### Step 5: 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:
\[ \frac{2\pi}{\lambda} = \frac{2\pi}{A} \]
Cancelling \( 2\pi \) from both sides, we find:
\[ \lambda = A \]

### Final Results
- The speed of the wave \( v \) is \( b \).
- The wavelength \( \lambda \) is \( A \).

### Summary
- Speed of the wave: \( v = b \)
- Wavelength: \( \lambda = A \)