Question

Explain the wave parameters in details.

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Solution

**Wave Parameters:**

1. The **wavelength** of a wave:

1.1 A wave consists of crests and trough which represents the maximum displacement of the particles of the wave undergoing a periodic motion.

1.2 The distance between these two consecutive crests or troughs is called the wavelength of a wave.

1.3 The wavelength of a wave is represented by the symbol $\lambda $.

1.4 If $v$ is the wave velocity and $f$ is the frequency, then wavelength $\lambda =\frac{v}{f}$.

2. **Amplitude** of a wave:

2.1 The maximum displacement suffered by the particle from its mean position due to the vibrational motion of the wave is called the amplitude.

2.2 The crest represents the amplitude in the positive axis.

2.3 The trough represents the amplitude in the negative axis.

3. **Time period** of a wave:

3.1 The total time taken for a particle of a wave to complete one whole periodic vibration is called the time period of a wave.

3.2 The time period of a wave is denoted as $T$.

3.3 The time period is always measured in seconds.

4. **Frequency** of a wave:

4.1 Frequency is the total number of complete oscillations traveled by a particle inside the wave.

4.2 The frequency of a wave is the reciprocal of the time period and is therefore measured in $Hz$ or ${s}^{-1}$.

4.3 If $f$ is the frequency of a wave, $f=\frac{1}{T}$.

4.4 If $v$ is the wave velocity and $f$ is the frequency, then using wavelength $f=\frac{v}{\lambda}$.

4.5 For the constant value of the velocity of the wave, the frequency of the wave is inversely proportional to the wavelength.

5. **Wave velocity:**

5.1 Wave velocity is the distance traveled by a particle of a wave per unit of time.

5.2 It is represented as $v=f\lambda $ where $\lambda $ is the wavelength of the wave and $f$ is the frequency.

5.3 The unit of wave velocity is $m{s}^{1}$.

6. **Phase difference** of a wave:

6.1 The difference in the periodic cycle of two waves is called the phase difference and it is represented by $\varphi $.

6.2 If two waves can overlap with each other without any phase difference, the waves are said to be in phase, or the angles between the two phases are equal.

6.3 If two waves cannot overlap upon each other and a phase difference is present, then they are said to be out of phase, or the angles between the two phases are unequal.

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