Loop lenght of a standing wave is 6cm. What is the phase difference between the two points separated by a distance of 2cm
1) 120
2) 180
3) 0
4) Either 0 or 180

To determine the phase difference between two points on a standing wave that are separated by a distance of 2 cm, we first need to understand the relationship between the wavelength, the distance between the points, and the phase difference. Given that the loop length of the standing wave is 6 cm, this means that the wavelength (λ) of the wave is also 6 cm, as a standing wave consists of nodes and antinodes along its length.

Understanding Wavelength and Phase Difference

The phase of a wave is typically measured in degrees or radians, and it indicates the position of a point in time on a waveform cycle. For a complete cycle, the phase difference is 360 degrees (or 2π radians). The phase difference (Δφ) between two points on a wave can be calculated using the formula:

Δφ = (Δx / λ) × 360°

Where:

• Δx is the distance between the two points.
• λ is the wavelength of the wave.

Calculating the Phase Difference

In this scenario:

• Δx = 2 cm
• λ = 6 cm

Now, substituting these values into the formula:

Δφ = (2 cm / 6 cm) × 360°

Calculating this gives:

Δφ = (1/3) × 360° = 120°

Interpreting the Result

The phase difference between the two points separated by 2 cm on the standing wave is 120 degrees. This means that one point is ahead of the other by 120 degrees in the wave cycle. Therefore, the correct answer to your question is:

1) 120

Why Not the Other Options?

• 180°: This would indicate that the two points are in opposite phases, which is not the case here.
• 0°: This would suggest that the two points are in phase, which is also not applicable given the distance of 2 cm.
• Either 0 or 180°: This option implies that the points could be in phase or completely out of phase, which does not align with the calculated phase difference of 120°.

In summary, the phase difference between the two points separated by a distance of 2 cm on a standing wave with a loop length of 6 cm is indeed 120 degrees. This understanding of phase differences is crucial in wave mechanics, as it helps in analyzing interference patterns and other wave phenomena.