# 12.2 Boundary conditions  (Page 5/5)

 Page 5 / 5

## Superposition and interference

1. For each labelled point, indicate whether constructive or destructive interference takes place at that point.
2. A ride at the local amusement park is called "Standing on Standing Waves". Which position (a node or an antinode) on the ride would give the greatest thrill?
3. How many nodes and how many anti-nodes appear in the standing wave below?
4. For a standing wave on a string, you are given three statements:
1. you can have any $\lambda$ and any $f$ as long as the relationship, $v=\lambda ·f$ is satisfied.
2. only certain wavelengths and frequencies are allowed
3. the wave velocity is only dependent on the medium
Which of the statements are true:
1. A and C only
2. B and C only
3. A, B, and C
4. none of the above
5. Consider the diagram below of a standing wave on a string 9 m long that is tied at both ends. The wave velocity in the string is 16 m $·$ s ${}^{-1}$ . What is the wavelength?

## Summary

1. A wave is formed when a continuous number of pulses are transmitted through a medium.
2. A peak is the highest point a particle in the medium rises to.
3. A trough is the lowest point a particle in the medium sinks to.
4. In a transverse wave, the particles move perpendicular to the motion of the wave.
5. The amplitude is the maximum distance from equilibrium position to a peak (or trough), or the maximum displacement of a particle in a wave from its position of rest.
6. The wavelength ( $\lambda$ ) is the distance between any two adjacent points on a wave that are in phase. It is measured in metres.
7. The period ( $T$ ) of a wave is the time it takes a wavelength to pass a fixed point. It is measured in seconds (s).
8. The frequency ( $f$ ) of a wave is how many waves pass a point in a second. It is measured in hertz (Hz) or $s{}^{-1}$ .
9. Frequency: $f=\frac{1}{T}$
10. Period: $T=\frac{1}{f}$
11. Speed: $v=f\lambda$ or $v=\frac{\lambda }{T}$ .
12. When a wave is reflected from a fixed end, the resulting wave will move back through the medium, but will be inverted. When a wave is reflected from a free end, the waves are reflected, but not inverted.

## Exercises

1. A standing wave is formed when:
1. a wave refracts due to changes in the properties of the medium
2. a wave reflects off a canyon wall and is heard shortly after it is formed
3. a wave refracts and reflects due to changes in the medium
4. two identical waves moving different directions along the same medium interfere
2. How many nodes and anti-nodes are shown in the diagram?
3. Draw a transverse wave that is reflected from a fixed end.
4. Draw a transverse wave that is reflected from a free end.
5. A wave travels along a string at a speed of $1,5m·s{}^{-1}$ . If the frequency of the source of the wave is 7,5 Hz, calculate:
1. the wavelength of the wave
2. the period of the wave
6. Water waves crash against a seawall around the harbour. Eight waves hit the seawall in 5 s. The distance between successive troughs is 9 m. The height of the waveform trough to crest is 1,5 m.
1. How many complete waves are indicated in the sketch?
2. Write down the letters that indicate any TWO points that are:
1. in phase
2. out of phase
3. Represent ONE wavelength.
3. Calculate the amplitude of the wave.
4. Show that the period of the wave is 0,67 s.
5. Calculate the frequency of the waves.
6. Calculate the velocity of the waves.

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
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?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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