The distance between two consecutive points with phase difference of `60^@` in a wave of frequency `500 Hz` is `6.0 m.` The velocity with which wave is a traveling is_______ km/s

Answer

To solve the problem, we need to find the velocity of the wave given the frequency and the distance between two points with a phase difference of 60 degrees.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Frequency (f) = 500 Hz
- Distance between points with a phase difference of 60° (Δx) = 6.0 m
- Phase difference (Δφ) = 60° = π/3 radians

2. **Relate Phase Difference to Wavelength:**
The relationship between phase difference and distance in terms of wavelength (λ) is given by:
\[ \Delta x = \frac{\lambda}{2\pi} \cdot \Delta \phi \]
Substituting the known values:
\[ 6.0 = \frac{\lambda}{2\pi} \cdot \frac{\pi}{3} \]

3. **Simplify the Equation:**
Rearranging the equation gives:
\[ 6.0 = \frac{\lambda}{6} \]
Therefore, multiplying both sides by 6:
\[ \lambda = 36.0 \text{ m} \]

4. **Use the Wave Velocity Formula:**
The wave velocity (v) can be calculated using the formula:
\[ v = f \cdot \lambda \]
Substituting the values of frequency and wavelength:
\[ v = 500 \, \text{Hz} \cdot 36.0 \, \text{m} = 18000 \, \text{m/s} \]

5. **Convert to km/s:**
To convert the velocity from meters per second to kilometers per second:
\[ v = \frac{18000 \, \text{m/s}}{1000} = 18 \, \text{km/s} \]

### Final Answer:
The velocity with which the wave is traveling is **18 km/s**.