Here we’ll look for mechanical waves-transverse and longitudinal waves. In transverse wave particles oscillate in perpendicular to direction of wave propagation and in longitudinal they oscillate in parallel with wave propagation. Wave equation is written as the displacement of particles at given time.
All terms in equation needs to understand like amplitude, frequency, phase, phase angle and wave number. Some of these quantities are inter-related like angular frequency- frequency. These inter-relations are important while solving problems. Given few parameters we can know all other from above equations. Also know about speed of different waves like wave on string or sound wave
.
Superposition of waves gives resultant displacement of particle at given position and time under two waves. We get resultant equation by adding two sinusoidal equations. We can derive equation for reflected waves from boundary. Equations may be different for rigid and non-rigid boundary. There is another wave pattern called standing or stationary wave resulting from superposing two waves travelling in opposite direction of same amplitude and wavelength.
Points with zero amplitude are nodes and other are antinodes. There are different modes and harmonics with which it can vibrate. Beats are also superposition of two waves of close frequencies. The result is beats with frequency equal to difference of their frequencies.
Know about its equation and characteristics. At last, Doppler’s effect comes into picture in which observed frequency of wave changes when source or observer moves relative to medium. There are three cases-source stationary observer moving, source moving observer stationary and source moving observer moving. In all these cases, we get equations. While using them, sign consideration is much important.
Mistakes/challenges–
- Understand difference between transverse and longitudinal clearly and terms related to them and how they are related to each other.
- Clear concepts about standing waves like they don’t move and energy also doesn’t get lost from them.
- Don’t confuse between modes and harmonics in standing wave. They differ by only one.
- Beats are also interference of waves but they require to certain conditions to occur.
- Remember in Doppler’s formula, sign will change if observer or source will move towards or away from each other.
Tips/guidelines-
- Practice to get information about wave from its given equation like frequency etc.
- Most of the times equations are given in problems.
- Also learn to get equation of wave after interference of two waves.
- Focus on standing waves, Doppler’s effect and somewhat about beats.
- Also better to know about speed of sound- a longitudinal wave and parameters on which it depends.
- Also read facts about waves for verbal questions like wave transfers energy not matter from one point to other.
The topic says about the mechanical waves and their properties. It defines wave, its reflection in terms of equation. We discussed superposition of waves of which standing wave and beats are one of the cases. And at last Doppler’s effect tells about the frequency if source or observer is moving relative to medium. It’s most important part and need to be focused.
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