Physics > Superposition of Waves > 2.0 Interference of Waves
Superposition of Waves
1.0 Introduction
2.0 Interference of Waves
2.1 Relation between phase difference $\left( \phi \right)$ and path difference $\left( {\Delta x} \right)$
2.2 Interference of waves from coherent sources
2.3 Interference of waves from incoherent sources
2.4 Reflection and transmission of a wave
2.5 Motion of wave during reflection
2.6 Expression for the reflection and transmission of wave
3.0 Standing or Stationary Wave
3.1 Transverse stationary wave on a stretched string
3.2 Vibrations in a stretched string
3.3 Melde's Experient
3.4 Resonance
4.0 Longitudinal stationary wave in an organ pipe
4.1 Open organ pipe
4.2 Closed organ pipe
4.3 End correction
4.4 Resonance tube
4.5 Energy in a stationary wave
5.0 Beats
6.0 Questions
2.4 Reflection and transmission of a wave
2.2 Interference of waves from coherent sources
2.3 Interference of waves from incoherent sources
2.4 Reflection and transmission of a wave
2.5 Motion of wave during reflection
2.6 Expression for the reflection and transmission of wave
3.2 Vibrations in a stretched string
3.3 Melde's Experient
3.4 Resonance
4.2 Closed organ pipe
4.3 End correction
4.4 Resonance tube
4.5 Energy in a stationary wave
Reflection and transmission of a wave take place at a boundary where two media separate from each other.
A medium is said to be denser (relative to other) if the speed of wave in this medium is less than the speed of wave in the other medium.
So, the speed of a wave in a denser medium is less than the speed in the rare medium.
So, $${v_{denser}} < {v_{rare}}$$
Note: Any medium can be denser for one type of wave and can be rare for the other type of wave.
For example: Wate is denser for electromagnetic waves as compared to air because the speed of electromagnetic waves is less in water than in air.
But water is a rare medium for sound waves as compared to air because the speed of sound wave in water is more.
Electromagnetic wave and sound wave both follow the law of refraction and reflection.
Law of reflection: Angle of incidence $(i)=$ angle of reflection $(r)$
Law of refraction: Refracted ray bend towards normal if it travels from a rare medium to a denser medium and vice-versa.
Physical quantities associated with a wave
| Wave property | Reflection | Refraction | Explanation |
| Velocity $(v)$ | does not change | changes | Speed of the wave depends on the medium and its characteristics. In reflection, the medium does not change, so the speed of wave does not change whereas in transmission, medium changes, so the speed of wave also changes. |
| Frequency $(f)$, Time period $(T)$ and Angular velocity $(\omega) $ | does not change | does not change | Frequency of the wave depends on the source from where wave originates. In reflection and transmission, since source does not change therefore the frequency does not change. Frequency $(f)$, time period $(T)$ and angular veloctity $(\omega) $ are related by, $$\omega = 2\pi f = \frac{{2\pi }}{T}$$ If frequency does not change, time period and angular velocity also does not change. |
| Wavelength $(\lambda)$, Wave number $(k)$ | does not change | changes | Relation of wavelength $(\lambda)$ and wave number $(k)$ is given by, $$k = \frac{{2\pi }}{\lambda }$$$$\lambda = \frac{v}{f}$$ During reflection, medium does not change. So, the velocity $v$ and frequency $f$ also does not change and therefore $(\lambda)$ & $k$ remains unchanged. During transmission, medium changes. So, the velocity $v$ changes and therefore$(\lambda)$ & $k$ also changes. |
| Amplitude $(A)$, Intensity $(I)$ | changes | changes | Intensity is the energy transmitted per unit area per unit time. $$\begin{equation} \begin{aligned} I = \frac{1}{2}{\omega ^2}{A^2}v \\ I \propto {A^2} \\\end{aligned} \end{equation} $$ When a wave is incident on a boundary separating two media, part of the wave is reflected and part is transmitted. Hence intensity and amplitude both change in reflection as well as transmission. Unless 100% reflection or 100% transmission takes place. |
| Phase $(\phi) $ | $\Delta \phi = 0$, when reflected from a rare medium $\Delta \phi = \pi $, when reflected from a denser medium | does not changes | In transmission no phase takes place. While in reflection, phase change is zero if the wave is reflected from a rare medium and if the wave is reflected from a denser medium phase change is $\pi $  |
