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Superposition of pulses

Two or more pulses can pass through the same medium at that same time in the same place. When they do they interact with each other to form a different disturbance at that point. The resulting pulse is obtained by using the principle of superposition . The principle of superposition states that the effect of the different pulses is the sum of their individual effects. After pulses pass through each other, each pulse continues along its original direction of travel, and their original amplitudes remain unchanged.

Constructive interference takes place when two pulses meet each other to create a larger pulse. The amplitude of the resulting pulse is the sum of the amplitudes of the two initial pulses. This is shown in [link] .

Constructive interference
Constructive interference is when two pulses meet, resulting in a bigger pulse.
Superposition of two pulses: constructive interference.

Destructive interference takes place when two pulses meet and cancel each other. The amplitude of the resulting pulse is the sum of the amplitudes of the two initial pulses, but the one amplitude will be a negative number. This is shown in [link] . In general, amplitudes of individual pulses add together to give the amplitude of the resultant pulse.

Destructive interference
Destructive interference is when two pulses meet, resulting in a smaller pulse.
Superposition of two pulses. The left-hand series of images demonstrates destructive interference, since the pulses cancel each other. The right-hand series of images demonstrate a partial cancelation of two pulses, as their amplitudes are not the same in magnitude.

The two pulses shown below approach each other at 1 m · s - 1 . Draw what the waveform would look like after 1 s , 2 s and 5 s .

  1. After 1 s , pulse A has moved 1 m to the right and pulse B has moved 1 m to the left.

  2. After 1 s more, pulse A has moved 1 m to the right and pulse B has moved 1 m to the left.

  3. After 5 s , pulse A has moved 5 m to the right and pulse B has moved 5 m to the left.

The idea of superposition is one that occurs often in physics. You will see much, much more of superposition!

Experiment: constructive and destructive interference

Aim

To demonstrate constructive and destructive interference

Apparatus

Ripple tank apparatus

Method

  1. Set up the ripple tank
  2. Produce a single pulse and observe what happens
  3. Produce two pulses simultaneously and observe what happens
  4. Produce two pulses at slightly different times and observe what happens

Results and conclusion

You should observe that when you produce two pulses simultaneously you see them interfere constructively and when you produce two pulses at slightly different times you see them interfere destructively.

Problems involving superposition of pulses

  1. For the following pulse, draw the resulting wave forms after 1 s , 2 s , 3 s , 4 s and 5 s . Each pulse is travelling at 1 m · s - 1 . Each block represents 1 m . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.
  2. For the following pulse, draw the resulting wave forms after 1 s , 2 s , 3 s , 4 s and 5 s . Each pulse is travelling at 1 m · s - 1 . Each block represents 1 m . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.
  3. For the following pulse, draw the resulting wave forms after 1 s , 2 s , 3 s , 4 s and 5 s . Each pulse is travelling at 1 m · s - 1 . Each block represents 1 m . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.
  4. For the following pulse, draw the resulting wave forms after 1 s , 2 s , 3 s , 4 s and 5 s . Each pulse is travelling at 1 m · s - 1 . Each block represents 1 m . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.
  5. For the following pulse, draw the resulting wave forms after 1 s , 2 s , 3 s , 4 s and 5 s . Each pulse is travelling at 1 m · s - 1 . Each block represents 1 m . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.
  6. For the following pulse, draw the resulting wave forms after 1 s , 2 s , 3 s , 4 s and 5 s . Each pulse is travelling at 1 m · s - 1 . Each block represents 1 m . The pulses are shown as thick black lines and the undisplaced medium as dashed lines.
  7. What is superposition of waves?
  8. What is constructive interference?
  9. What is destructive interference?

The following presentation provides a summary of the work covered in this chapter. Although the presentation is titled waves, the presentation covers pulses only.

Summary

  • A medium is the substance or material in which a wave will move
  • A pulse is a single disturbance that moves through a medium
  • The amplitude of a pules is a measurement of how far the medium is displaced from rest
  • Pulse speed is the distance a pulse travels per unit time
  • Constructive interference is when two pulses meet and result in a bigger pulse
  • Destructive interference is when two pulses meet and and result in a smaller pulse
  • We can draw graphs to show the motion of a particle in the medium or to show the motion of a pulse through the medium
  • When a pulse moves from a thin rope to a thick rope, the speed and pulse length decrease. The pulse will be reflected and inverted in the thin rope. The reflected pulse has the same length and speed, but a different amplitude
  • When a pulse moves from a thick rope to a thin rope, the speed and pulse length increase. The pulse will be reflected in the thick rope. The reflected pulse has the same length and speed, but a different amplitude
  • A pulse reaching a free end will be reflected but not inverted. A pulse reaching a fixed end will be reflected and inverted

Exercises - transverse pulses

  1. A heavy rope is flicked upwards, creating a single pulse in the rope. Make a drawing of the rope and indicate the following in your drawing:
    1. The direction of motion of the pulse
    2. Amplitude
    3. Pulse length
    4. Position of rest
  2. A pulse has a speed of 2,5 m · s - 1 . How far will it have travelled in 6 s ?
  3. A pulse covers a distance of 75 cm in 2,5 s . What is the speed of the pulse?
  4. How long does it take a pulse to cover a distance of 200 mm if its speed is 4 m · s - 1 ?
  5. The following position-time graph for a pulse in a slinky spring is given. Draw an accurate sketch graph of the velocity of the pulse against time.
  6. The following velocity-time graph for a particle in a medium is given. Draw an accurate sketch graph of the position of the particle vs. time.
  7. Describe what happens to a pulse in a slinky spring when:
    1. the slinky spring is tied to a wall.
    2. the slinky spring is loose, i.e. not tied to a wall.
    (Draw diagrams to explain your answers.)
  8. The following diagrams each show two approaching pulses. Redraw the diagrams to show what type of interference takes place, and label the type of interference.
  9. Two pulses, A and B, of identical shape and amplitude are simultaneously generated in two identical wires of equal mass and length. Wire A is, however, pulled tighter than wire B. Which pulse will arrive at the other end first, or will they both arrive at the same time?

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
Mukesh Reply
Properties of longitudinal waves
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Source:  OpenStax, Siyavula textbooks: grade 10 physical science [caps]. OpenStax CNX. Sep 30, 2011 Download for free at http://cnx.org/content/col11305/1.7
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