Are Beats and Standing Waves Related in Physics?

In summary, transverse waves have nodes, beats have harmonics, and the tones produced in case of beats also depends upon whether for e.g.closed and open organ pipes but I'm messed up with displacement and pressure nodes as you don't have pressure nodes in transverse waves.)
  • #1
Bilbo B
9
1
TL;DR Summary
How does the standing waves relate to beats? There are nodes and antinodes in case of standing waves but how these nodes are related to find harmonics. The factors whether a string fixed at both ends or fixed at single end decides it's nature.
If the standing waves for beats are the longitudinal ones. what are the basis for differentiating from transverse.The beats have also nodes, there is a difference such from the transverse waves.Do they too have harmonics? the tones produced in case of beats also depends upon whether for e.g.closed and open organ pipes but I'm messed up with displacement and pressure nodes as you don't have pressure nodes in transverse waves. Beats if an elaborate extension of longitudinal waves, Can i consider them as same.
If the frequencies in transverse waves are integer multiples of lowest frequency, how they physically represent tones and harmonics.
 
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  • #2
I think you would need to specify which waves you are discussing. In elementary wave theory, it's normal to consider either ideal transverse ( ideal strings) or ideal longitudinal wave models (ideal organ pipes).
Also I don't know what you mean by standing waves for beats. In a simple model, the various modes are independent. Perhaps if you told us the actual problem then it may trigger some useful thoughts.
Edit:
PS it's as well to start off on the right foot here. The higher modes in most cases are not actual harmonics ( not 2f,3f,4f etc). The natural frequencies are a function of the wavelengths and the effective length of a resonator and the family of higher frequency resonances are actually (should be) referred to as Overtones. They can be waaay off the harmonic frequencies.
 
  • #3
Harmony is natures way of producing waves other than a sine, combined with a sine. It can be produced by many factors. An instrumental string in motion, is in many occasions in a super position, producing different wave lengths at the same time. I recommend you to read about analogue synthesizers for example. When it comes to standing waves, this is only an expression of trapped waves. For example waves in a corner bouncing forward and backwords that are not going anywhere.

The waves are all the same in different wavelengths and amplitude. This is why these lengths of waves are mostly perceived by your eardrum. Light and photons are also vibration, in many forms, only perceptible by your eyes.
 
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  • #4
Solomei said:
Harmony is natures way of producing waves other than a sine, combined with a sine. It can be produced by many factors. An instrumental string in motion, is in many occasions in a super position, producing different wave lengths at the same time. I recommend you to read about analogue synthesizers for example. When it comes to standing waves, this is only an expression of trapped waves. For example waves in a corner bouncing forward and backwords that are not going anywhere.

The waves are all the same in different wavelengths and amplitude. This is why these lengths of waves are mostly perceived by your eardrum. Light and photons are also vibration, in many forms, only perceptible by your eyes.
What is all that supposed to be about? Is there any actual Physics buried in there or did you just have a yearning to write a purple passage?
 

1. What are beats and standing waves?

Beats and standing waves are two concepts in physics that relate to the way that waves interact with each other. Beats occur when two waves with slightly different frequencies interfere with each other, resulting in a pulsing pattern. Standing waves, on the other hand, are stationary patterns that form when two waves with the same frequency interfere with each other.

2. How do beats and standing waves differ?

Beats and standing waves differ in their frequency and the resulting pattern. Beats have a frequency equal to the difference between the two interfering waves, while standing waves have the same frequency as the individual waves. Additionally, beats have a pulsing pattern, while standing waves have a stationary pattern.

3. What causes beats and standing waves?

Beats are caused by the interference of two waves with slightly different frequencies. This results in constructive and destructive interference, creating a pulsing pattern. Standing waves are caused by the interference of two waves with the same frequency, resulting in a stationary pattern due to the reinforcement of the waves.

4. What are some real-life examples of beats and standing waves?

Beats can be heard in music when two instruments or voices play/sing slightly out of tune with each other. Standing waves can be seen in musical instruments, such as a guitar string or a pipe organ, where the waves reflect off the ends of the instrument and create a stationary pattern.

5. How are beats and standing waves used in science and technology?

Beats and standing waves have many practical applications in science and technology. They are used in fields such as acoustics, optics, and telecommunications. For example, beats are used in tuning instruments and in noise-cancelling headphones, while standing waves are used in lasers and fiber optics for data transmission.

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