Reflection of a pulse from fixed and free ends (not in caps - included for completeness)
Let us now consider what happens to a pulse when it reaches the end of a medium. The medium can be fixed, like a rope tied to a wall, or it can be free, like a rope tied loosely to a pole.
Reflection of a pulse from a fixed end
Investigation : reflection of a pulse from a fixed end
Tie a rope to a wall or some other object that cannot move. Create a pulse in the rope by flicking one end up and down. Observe what happens to the pulse when it reaches the wall.
When the end of the medium is fixed, for example a rope tied to a wall, a pulse reflects from the fixed end, but the pulse is inverted (i.e. it is upside-down). This is shown in
[link] .
Reflection of a pulse from a free end
Investigation : reflection of a pulse from a free end
Tie a rope to a pole in such a way that the rope can move up and down the pole. Create a pulse in the rope by flicking one end up and down. Observe what happens to the pulse when it reaches the pole.
When the end of the medium is free, for example a rope tied loosely to a pole, a pulse reflects from the free end, but the pulse is
not inverted . This is shown in
[link] . We draw the free end as a ring around the pole. The ring will move up and down the pole, while the pulse is reflected away from the pole.
The fixed and free ends that were discussed in this section are examples of
boundary conditions . You will see more of boundary conditions as you progress in the Physics syllabus.
Pulses at a boundary ii
A rope is tied to a tree and a single pulse is generated. What happens to the pulse as it reaches the tree? Draw a diagram to explain what happens.
A rope is tied to a ring that is loosely fitted around a pole. A single pulse is sent along the rope. What will happen to the pulse as it reaches the pole? Draw a diagram to explain your answer.
The following simulation will help you understand the previous examples. Choose pulse from the options (either manual, oscillate or pulse). Then click on pulse and see what happens. Change from a fixed to a free end and see what happens. Try varying the width, amplitude, damping and tension.
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
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:
The direction of motion of the pulse
Amplitude
Pulse length
Position of rest
A pulse has a speed of
. How far will it have travelled in
?
A pulse covers a distance of
in
. What is the speed of the pulse?
How long does it take a pulse to cover a distance of
if its speed is
?
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.
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.
Describe what happens to a pulse in a slinky spring when:
the slinky spring is tied to a wall.
the slinky spring is loose, i.e. not tied to a wall.
(Draw diagrams to explain your answers.)
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.
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
differentiate between demand and supply
giving examples
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
When MP₁ becomes negative, TP start to decline.
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 •
Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Economic growth as an increase in the production and consumption of goods and services within an economy.but
Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has
The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50.
A,Calculate quantities of x and y which maximize utility.
B,Calculate value of Lagrange multiplier.
C,Calculate quantities of X and Y consumed with a given price.
D,alculate optimum level of output .
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product