# MHT-CET Physics Crash Course “Formation of Stationary Waves” Class 12

## “Formation of Stationary Waves” MHT-CET Class 12 Physics Crash Course | Chapter – Superposition of Waves

In this session G.S. Khairnar discussed the theory and MCQ’s of “Formation of Stationary Waves”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.

### Formation of Stationary Waves:-

Hello dear students in previous article we had learnt about the reflection of transverse and longitudinal waves. Now we all know that the waves get reflected from denser as well as rarer medium with some important changes. As we know that in reflection of transverse wave from denser medium, crest is reflected as trough and vice versa. Whereas in reflection from rarer medium crest reflected as crest and same for trough too. Due to reflection the phase of waves changes by 1800. In this article we will discuss about some important aspects about the reflection of waves with the help of principal of superposition of waves.

• Principle of superposition of Waves:

When two or more waves travelling through a medium arrive at a point of the medium simultaneously each wave produced its own displacement at the point independently of the other and the resultant displacement at the point is equal to the vector sum of the displacement due to all the waves.

• Stationary Waves:

When two identical progressive waves travelling through the same medium, along same starlight line in the opposite direction, the stationary waves are produced.

Note:

1. Stationary waves do not travel in any direction.
2. Stationary waves do not transfer energy through medium.
3. These waves are also called standing waves.

Let’s learn the formation of stationary waves by analytical method….!

Consider two progressive waves of same amplitude a period T, wavelength λ & speed v are travelling through the same medium, along but opposite in direction.

A progressive wave travelling along positive direction of x-axis is represented by

The resultant wave is called stationary wave or standing wave.

Antinode:-

The points of medium at which the amplitude of vibration of particle maximum are called antinodes.

Node: –

The point of medium at which the amplitude of vibrations of particles is zero are called nodes.

i.e. the distance between adjacent node and antinode is

In stationary waves nodes and antinodes are alternatively placed in medium.

• Characteristic of stationary waves:-
1. When two identical progressive waves travelling through the medium along the same line in opposite direction, the stationary waves are formed.
2. The point where amplitude is maximum, called antinodes.
3. The points where amplitude is zero are called nodes.
4. The distance between two successive nodes or antinodes is .
5. The distance between node & adjacent antinodes is
6. All points of the medium except nodes perform SHM.
7. The amplitude of SHM is not same for all particles. It increases from node to antinodes.
8. All the particles in one loop are in the same phase. While particles in the adjacent loops are out on phase ( i.e. phase difference is  rad)
9. The pressure changes are zero at displacement antinodes, So displacement antinodes are pressure nodes.
10. The pressure change is maximum at displacement nodes hence displacement nodes are pressure antinodes

### ♦जिल्हा नुसार जाहिराती ♦

अहमदनगर अकोला अमरावती औरंगाबाद भंडारा बुलढाणा
चंद्रपुर धुले गढ़चिरौली गोंदिया हिंगोली जलगांव
जालना कोल्हापुर लातूर मुंबई नागपुर नांदेड़
नंदुरबार नाशिक उस्मानाबाद पालघर परभानी पुणे
रायगढ़ रत्नागिरि सांगली सातारा सिंधुदुर्ग सोलापुर
ठाणे वर्धा वाशिम यवतमाल बीड

### ♦शिक्षणानुसार जाहिराती ♦

७ वी (7th) दहावी (SSC) बारावी (HSC) डिप्लोमा आय.टी.आय पदवी
पदव्युत्तर शिक्षण बी.एड एम.एड एल.एल.बी / एल.एल.एम बीएससी एमबीए
बीसीए एमसीए बी.कॉम एम.कॉम GNM/ANM एमएससी
बी.फार्म एम.फार्म बी.ई एम.ई BAMS/BHMS एम.बी.बी.एस / एम.डी
बी.टेक एम.टेक MS-CIT