Comparing Standing Waves, Beats & Interference of Waves

[raghavK.dua]

1)What is the difference between standing waves,beats and normal interference of any 2 waves ?
2)Is beats in sound waves same as interference in light waves ?
3)Why do we represent particle displacement with y and wave motion with x in longitudnal waves in which both particle and wave motion occur in same direction ?

 

[tiny-tim]

hi raghavK.dua! welcome to pf!

2)Is beats in sound waves same as interference in light waves ?

basically, yes

3)Why do we represent particle displacement with y and wave motion with x in longitudnal waves in which both particle and wave motion occur in same direction ?

you have to call them something

what else would you call them?

you could use x and x_rel …

but x and y is much easier to write ​

1)What is the difference between standing waves,beats and normal interference of any 2 waves ?

tell us what you think, and then we'll comment!

 

[BruceW]

3)Why do we represent particle displacement with y and wave motion with x in longitudnal waves in which both particle and wave motion occur in same direction ?

I often use 'u' as particle displacement. no real reason, except that I don't like using y.

 

[raghavK.dua]

tell us what you think, and then we'll comment!

As far as I have understood for beats the 2 waves should have nearly same frequency.In standing waves 2 waves of same frequency and amplitude moving in opposite direction have to interfere.My questions are:-

1)After normal interference transfer of energy takes place as the resultant wave travels but in standing wave no transfer of energy takes place.why?

2)In standing waves all the particle achieve maxima at same instant why doesn't this happen in a wave which is formed due to normal interference.

3)Point of maxima and minima are there in every type of wave what's so special about beats ?

 

[sophiecentaur]

3)Point of maxima and minima are there in every type of wave what's so special about beats ?

Beats are a variation in time, as opposed to the unchanging interference pattern when only one frequency is involved. The pattern from two or more sources with different frequencies will be in motion all the time. It will consist of moving Moiree type fringes, the spacing and speed will relate to the frequency difference.

 

[dauto]

Beats are the result of interfering two waves with slightly different frequencies.

 

[olivermsun]

As far as I have understood for beats the 2 waves should have nearly same frequency.In standing waves 2 waves of same frequency and amplitude moving in opposite direction have to interfere.My questions are:-

1)After normal interference transfer of energy takes place as the resultant wave travels but in standing wave no transfer of energy takes place.why?

The 2 waves that make up the standing wave have equal flux magnitudes but in opposite directions ($\textbf{F}$ and $-\textbf{F}$), so that the net flux is $-\textbf{F} + \textbf{F} = \textbf{0}.$

2)In standing waves all the particle achieve maxima at same instant why doesn't this happen in a wave which is formed due to normal interference.

Well, one way to think of it is that if the wave crests (maxima) were observed at different places at different times, then the combined wave would be propagating and not standing.

3)Point of maxima and minima are there in every type of wave what's so special about beats ?

I suppose beats are interesting for lots of reasons, one of which is that they come straight out of trig identities, but they have an interesting real-world presentation as well. When you put together two waves which are close together in frequency, you typically stop perceiving the waves separately and instead notice the "average" wave and its beats. Similarly with "spatial" beats, which also happen.