The wave equation is `y=0.30 sin (314 t-1.57 x)` where t , x and y are in second, meter and centimeter respectively. The speed of the wave is

Options

A. `100 m//s`
B. `200 m//s`
C. ` 300m//s`
D. `400 m//s`

Answer

To find the speed of the wave given the wave equation \( y = 0.30 \sin(314t - 1.57x) \), we can follow these steps:

### Step 1: Identify the wave equation parameters
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.

From the given equation \( y = 0.30 \sin(314t - 1.57x) \):
- The amplitude \( A = 0.30 \) cm,
- The angular frequency \( \omega = 314 \) rad/s,
- The wave number \( k = 1.57 \) rad/m.

### Step 2: 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 \( k \):
\[ v = \frac{314}{1.57} \]

### Step 3: Perform the calculation
Now, we will perform the division:
\[ v = \frac{314}{1.57} \approx 200 \text{ m/s} \]

### Conclusion
Thus, the speed of the wave is approximately \( 200 \) m/s.

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