From a wave equation
`y= 0.5 sin ((2pi)/3.2)(64t-x).`
the frequency of the wave is

Options

A. 5 Hz
B. 15 Hz
C. 20 Hz
D. 25 Hz

Answer

To find the frequency of the wave given by the equation \( y = 0.5 \sin\left(\frac{2\pi}{3.2}(64t - x)\right) \), we can follow these steps:

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

### Step 2: Compare the given equation with the standard form
From the given equation:
\[ y = 0.5 \sin\left(\frac{2\pi}{3.2}(64t - x)\right) \]
we can rewrite it as:
\[ y = 0.5 \sin\left(\frac{2\pi}{3.2} \cdot 64t - \frac{2\pi}{3.2} \cdot x\right) \]
This allows us to identify:
- \( \omega = \frac{2\pi}{3.2} \cdot 64 \)
- \( k = \frac{2\pi}{3.2} \)

### Step 3: Calculate the angular frequency \( \omega \)
Now, we can calculate \( \omega \):
\[ \omega = \frac{2\pi}{3.2} \cdot 64 \]

### Step 4: Calculate the frequency \( f \)
The relationship between angular frequency \( \omega \) and frequency \( f \) is given by:
\[ \omega = 2\pi f \]
From this, we can express frequency as:
\[ f = \frac{\omega}{2\pi} \]

### Step 5: Substitute \( \omega \) into the frequency formula
Substituting the expression for \( \omega \):
\[ f = \frac{\frac{2\pi}{3.2} \cdot 64}{2\pi} \]
The \( 2\pi \) cancels out:
\[ f = \frac{64}{3.2} \]

### Step 6: Calculate the final frequency
Now, we perform the division:
\[ f = 20 \text{ Hz} \]

Thus, the frequency of the wave is \( 20 \text{ Hz} \).

### Final Answer:
The frequency of the wave is \( 20 \text{ Hz} \).

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