The displacement y of a wave travelling in the x-direction is given by
`y = 10^(-4) sin (600t - 2x + (pi)/(3)) m`
Where x is expressed in metre and t in seconds. The speed of the wave motion in m/s is

Options

A. 300
B. 600
C. 1200
D. 200

Explanation

To find the speed of the wave motion given the displacement equation, we can follow these steps:

### Step 1: Identify the wave equation
The displacement of the wave is given by:
\[ y = 10^{-4} \sin(600t - 2x + \frac{\pi}{3}) \]

### Step 2: Compare with the standard wave equation
The standard form of a wave equation is:
\[ y = A \sin(\omega t - kx + \phi) \]
where:
- \( A \) is the amplitude,
- \( \omega \) is the angular frequency,
- \( k \) is the wave number,
- \( \phi \) is the phase constant.

From the given equation, we can identify:
- Amplitude \( A = 10^{-4} \) m
- Angular frequency \( \omega = 600 \) rad/s
- Wave number \( k = 2 \) rad/m
- Phase constant \( \phi = \frac{\pi}{3} \)

### Step 3: Calculate the speed of the wave
The speed \( v \) of the wave can be calculated using the relationship:
\[ v = \frac{\omega}{k} \]

Substituting the values we identified:
\[ v = \frac{600 \, \text{rad/s}}{2 \, \text{rad/m}} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ v = 300 \, \text{m/s} \]

### Conclusion
The speed of the wave motion is:
\[ \boxed{300 \, \text{m/s}} \]

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