The phase of particle at t is 70°and another particle is at t is 790° what is wavelength if the distance between two particles is1 m

To find the wavelength of the particles based on their phase differences and the distance between them, we can use some fundamental concepts from wave physics. Let's break this down step by step.

Understanding Phase Difference

The phase of a wave is a measure of the position of a point in time on a waveform cycle. In this case, we have two particles with phases of 70° and 790°. First, we need to determine the phase difference between these two particles.

Calculating Phase Difference

To find the phase difference, we can subtract the smaller phase from the larger one:

• Phase of Particle 1 = 70°
• Phase of Particle 2 = 790°

Since 790° is greater than 360°, we can simplify it by subtracting 360° to find its equivalent phase within one cycle:

• 790° - 360° = 430°
• 430° - 360° = 70° (which is equivalent to 70°)

Now, the phase difference is:

• Phase Difference = 70° - 70° = 0°

This means that both particles are in phase with each other.

Relating Phase Difference to Wavelength

The relationship between phase difference and wavelength is crucial. The phase difference (in radians) can be expressed as:

Phase Difference (in radians) = (2π / λ) * distance

Where λ is the wavelength and distance is the separation between the two particles. Since we have a phase difference of 0°, we can convert this to radians:

• 0° = 0 radians

Finding the Wavelength

Substituting the values into the equation:

0 = (2π / λ) * 1 m

Since the phase difference is 0, this indicates that the particles are perfectly in sync, and we cannot directly determine the wavelength from this equation alone. However, if we consider that the particles are part of a continuous wave, we can infer that the wavelength can be any value, as they are oscillating together.

Conclusion

In summary, the phase difference of 0° means that the two particles are in phase, and without additional information about the wave properties (like frequency or speed), we cannot determine a specific wavelength. The distance of 1 m simply indicates how far apart they are, but it does not provide enough information to calculate a unique wavelength. If you have more details about the wave, such as its frequency or speed, we could find the wavelength more precisely.