# Waves path and phase difference relationship

### Phase (waves) - Wikipedia

The two wave crests are taking two different paths to the same location to . variety of antinodal and nodal points on a typical pattern reveals the above relationships. Two point sources, cm apart, are generating periodic waves in phase. The relationship between period, frequency, and amplitude for a sine wave is illustrated in this image. Phase is the position of a point in time (an instant) on a waveform cycle. A complete cycle is In sinusoidal functions or in waves, "phase " has two different, but closely related, meanings. One is the initial angle of a. Thus, we say that, there is a path difference between the two waves of about λ ( wavelength). It has a direct relation with phase difference.

If the source of waves produces circular waves, then the circular wavefronts will meet within the medium to produce a pattern.

**Graphical Representation of Wave: Phase Difference**

The pattern is characterized by a collection of nodes and antinodes that lie along nearly straight lines referred to as antinodal lines and nodal lines. If the wave sources have identical frequencies, then there will be an antinodal line in the exact center of the pattern and an alternating series of nodal and antinodal lines to the left and the right of the central antinodal line.

As discussed in the previous section of Lesson 3each line in the pattern is assigned a name e.

A representative two-point source interference pattern with accompanying order numbers m values is shown below. In this part of Lesson 3, we will investigate the rationale behind the numbering system and develop some mathematical equations that relate the features of the pattern to the wavelength of the waves.

This investigation will involve the analysis of several antinodal and nodal locations on a typical two-point source interference pattern. It will be assumed in the discussion that the wave sources are producing waves with identical frequencies and therefore identical wavelengths.

## The Path Difference

To begin, consider the pattern shown in the animation below. Point A is a point located on the first antinodal line. This specific antinode is formed as the result of the interference of a crest from Source 1 S1 meeting up with a crest from Source 2 S2.

The two wave crests are taking two different paths to the same location to constructively interfere to form the antinodal point. The crest traveling from Source 1 S1 travels a distance equivalent to 5 full waves; that is, point A is a distance of 5 wavelengths from Source 1 S1.

### The Path Difference

The crest traveling from Source 2 S2 travels a distance equivalent to 6 full waves; point A is a distance of 6 wavelengths from Source 2 S2. While the two wave crests are traveling a different distance from their sources, they meet at point A in such a way that a crest meets a crest.

Phase difference is the difference, expressed in degrees or radians, between two waves having the same frequency and referenced to the same point in time. Two oscillators that have the same frequency and different phases have a phase difference, and the oscillators are said to be out of phase with each other.

If two interacting waves meet at a point where they are in antiphase, then destructive interference will occur. It is common for waves of electromagnetic light, RFacoustic sound or other energy to become superposed in their transmission medium. When that happens, the phase difference determines whether they reinforce or weaken each other. Complete cancellation is possible for waves with equal amplitudes.

### Wave Motion | - relation between phase difference and path-askIITians

Time is sometimes used instead of angle to express position within the cycle of an oscillation. A phase difference is analogous to two athletes running around a race track at the same speed and direction but starting at different positions on the track.

They pass a point at different instants in time. But the time difference phase difference between them is a constant - same for every pass since they are at the same speed and in the same direction.

## Phase (waves)

If they were at different speeds different frequenciesthe phase difference is undefined and would only reflect different starting positions. Technically, phase difference between two entities at various frequencies is undefined and does not exist. Time zones are also analogous to phase differences.