A transverse wave propagating along x-axis is represented by: `y(x,t)=8.0sin(0.5pix-4pit-(pi)/(4))` Where `x` is in metres and `t` is in seconds. The speed of the wave is:

Options

A. `4pim//s`
B. `0.5pi m//s`
C. `pi//4m//s`
D. `8 m//s`

Explanation

To find the speed of the transverse wave represented by the equation \( y(x,t) = 8.0 \sin(0.5\pi x - 4\pi t - \frac{\pi}{4}) \), we can follow these steps:

### Step 1: Identify the wave parameters
The general form of a transverse wave can be expressed as:
\[ y(x,t) = A \sin(kx - \omega t + \phi) \]
where:
- \( A \) is the amplitude,
- \( k \) is the wave number,
- \( \omega \) is the angular frequency,
- \( \phi \) is the phase constant.

From the given equation, we can identify:
- Amplitude \( A = 8.0 \) m,
- Wave number \( k = 0.5\pi \) rad/m,
- Angular frequency \( \omega = 4\pi \) rad/s.

### Step 2: Calculate the speed of the wave
The speed \( v \) of a wave is given by the relationship:
\[ v = \frac{\omega}{k} \]

Substituting the values of \( \omega \) and \( k \):
\[ v = \frac{4\pi}{0.5\pi} \]

### Step 3: Simplify the expression
Now simplify the expression:
\[ v = \frac{4\pi}{0.5\pi} = \frac{4}{0.5} = 8 \text{ m/s} \]

### Conclusion
The speed of the wave is:
\[ v = 8 \text{ m/s} \]

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