Wave behaviour Flashcards
What is simple harmonic motion
Acceleration is directly proportional to displacement in a negative direction, from a fixed point and has always directed to that fixed point
What is an oscillation
Repetitive variation of the displacement of an object about the equilibrium
How do you make a pendulum swing quicker
A pendulum is only dependent on length therefore if you shorten the length the pendulum will swing quicker
For a pendulum what would the graph for displacement against time look like
The graph would start at a positive displacement and would curve down to create a minimum in the negative values before curving up to create a maximum before coming down again, and so on. It will look a little bit like a cos graph
On a displacement graph for a pendulum what does the roots of the graph mean, and what does the max and min areas of the graph mean
The roots of the graph mean the equilibrium points where displacement equals zero, the maximum and minimum points show the highest displacement of the pendulum
What is the amplitude
Displacement on either side of the graph. Measured in metres
What is wavelength
The distance between two successive points on a graph for example from peak to Peak or trough to trough
What is a period
The time interval for one complete oscillation measured in seconds
What is it called if the oscillations have a constant period
This is called isochronos. This means all cycles are at the same period
What is frequency
The number of oscillations per second measured in Hertz or Hz
What is angular frequency
The rate of change of angular displacement with respect to time (rads^-1)
How do you convert milliseconds into seconds
divide the milliseconds by 1000
How do you convert from radians to degrees and vice versa. What is a good way to remember this?
To convert radians to degrees:
Radians = pi/180 x degrees
Degrees = 180/pi x radians
- To convert radians to degrees, pi should be on the numerator
- to convert from degrees to radians, 180° should be on the numerator
What is the force responsible for the motion in simple harmonic motion
Restoring force. This force is always directed towards the equilibrium point
What is acceleration directly proportional to in simple harmonic motion
Acceleration is directly proportional to displacement in the negative direction
The acceleration against displacement graph look like for simple harmonic motion
There should be a straight diagonal line with a negative gradient going through the origin. It should start at the top of the second quadrant and end at the bottom of the fourth quadrant
Why is a person jumping on a trampoline not an example of simple harmonic motion
- the restoring force is equal to their weights which is constant
– on a trampoline, the jumper can always jump higher and change displacement which is not allowed for simple harmonic motion
– the restoring force on the person is not proportional to the distance from the equilibrium position
What are the conditions for simple harmonic motion
- the restoring force is proportional to the displacement (this means that X force, should only take me to a Y displacement)
– the restoring force is opposite to the direction of the displacement
What do the displacement, velocity, and acceleration graphs look like against time for a pendulum? And how can you remember that?
For displacement:
The graph would look like a cos graph, where the roots are where the pendulum is at the equilibrium point and the maximum and minimum is when the pendulum is at its maximum displacement
for Velocity:
The velocity graph will look like a sign graph that has been reflected in the x axis. On this graph minimum and maximum points will be when the pendulum is at its equilibrium .
For acceleration:
The graph will look like a cos graph reflected in the x axis. At the roots of the graph is the equilibrium point of the pendulum
How to remember them:
For displacement, you start at the top
For velocity, you start at the middle
For acceleration, you start at the bottom
When is the displacement highest on a pendulum?
When it has been pulled up to its maximum height
When is the velocity highest on a pendulum? why
At the equilibrium point. As the pendulum swings down from its maximum displacement (the highest point), gravitational potential energy is converted into kinetic energy.
At the equilibrium position, all the available potential energy has been converted into kinetic energy, meaning the pendulum reaches its maximum speed.
After passing through the equilibrium position, the pendulum starts to swing upward, and the kinetic energy begins converting back into potential energy, causing the velocity to decrease.
When is acceleration highest on a pendulum? and why?
At the end points, the pendulum momentarily stops before reversing direction, meaning its velocity is zero.
However, the force pulling the pendulum back toward the center (due to gravity) is greatest at these points, creating the maximum acceleration.
This acceleration is directed toward the center (the equilibrium position), and it is entirely due to the restoring force acting along the path of the swing.
What does the graph look like for potential energy against time
The graph will start at a positive Y value before curving down to the X axis before curving back up to create a maximum point and so on. The graph will never go below the axis, because energy can never be negative
What does the graph look like for kinetic energy against time
The graph will start at the origin and curve straight up to make a maximum before coming back down to the X axis. This will repeat. The graph will never cross the axis because energy can never be negative. at the max points of the graph resembles the equilibrium point
What does the graph look like for total energy against time
Draw the graph for potential energy against time. On top of it draw the graph for kinetic energy against time. a horizontal line that touches the peaks of both the graphs. This horizontal line is your total energy
For a mass on a spring, how far is one period
Let’s say the minimum displacement is A, the equilibrium point is B and the maximum displacement is C. one period is always from A back to A again or C back to C again
What three things are required to calculate simple harmonic motion in a practical
– A spring or a pendulum
– a stopwatch
– up to 10 oscillations
How do you get the equation theta = arc length/ radius
w = theta/t
v = s/t
v = wr
therefore:
w = v/r
v/r = theta/t
t = v/s
v/r = stheta/v
the velocities cancel,
1/r = stheta
therefore
theta = s/r
What is the formula for displacement, velocity and acceleration in terms of amplitude
x = Acos (wt)
v = -Awsin(wt)
a = -Aw^2cos(wt)
derive displacement to get the velocity. Derive velocity to get acceleration. Use the chain rule
What are the three types of energy in simple harmonic motion
Elastic
Potential
Kinetic
Chemical (chemical energy in the bonds of the molecules)
What is a wave
A disturbance that carries energy through matter or space
What is a medium
Matter through which a wave travels
What moves, energy or matter in a wave
Matter doesn’t move but energy does
What is a transverse wave plus example
A wave where the oscillations are perpendicular to the waves motion. For example light waves or ripples in a pond
What is a longitudinal wave plus example
Where the oscillations are parallel to the direction of wave motion for example sound waves
On a soundwave graph, what does the peak and the trough represent
The peak represents compression and the trough represents rarefaction
How does amplitude affect energy and sound
The larger the amplitude the more energy, therefore the loud at the sound, and vice versa
How does wavelengths affect energy
The longer the wavelengths the less energy there is. They are inversely proportional
How does wavelength affect frequency
Wavelengths there is lower frequency. This is because at long wavelength the period is longer, and because frequency is 1/ period, the higher the period the lower the frequency
What is the formula for wave speed
Wave speed = frequency x wavelength
How is pitch related to frequency
At high pitches, there is a high frequency and vice versa
How does wavelength relate to pitch
Longer wavelength there is a lower pitch
What is a standing wave
Waves that are not moving
What are nodes and antinodes? And what is the relationship with movement
nodes are where there is no movement in the standing wave, and antinodes are where there is maximum movement in the standing wave
A microwave is an example of a standing wave. What happens to the food at the nodes and at the anti-nodes
At the nodes:
The food heats up less
at the antinodes:
The food is heated up more
This is why a microwave has a rotating plate, so that the food is evenly heated
What is resonance
Resonance occurs when a system is subjected to an oscillating force at a frequency that matches its natural frequency.
When there is an open pipe should the sound wave start at a node or an antinode? why?
It should start at an antinode. This is because a soundwave is longitudinal, so the particles have to move in the direction of energy transfer. This could only happen at antinodes
What does the first harmonic for an open pipe resonance look like
It should be from one anti-node to another that spans half a wavelength
What is a harmonic
The frequency for which you get a standing wave
What is the formula that ties together length wavelengths and harmonic
L = n x lambda/2
where:
L = length of pipe
n = harmonic
lambda = wavelength
What do the wavelengths go up in for an open pipe resonance
It goes up in halves
What does the first harmonic look like for a pipe that is closed at one end
It has a note at one end and opens up to an anti-node at the other there should be 1/4 of a wavelength
What do the wavelengths go up in for a closed ended pipe? And why does it not include even numbers
The wave lengths go up in halves, starting from 1/4. There is no 2/4 wavelengths because this means the wave would have a wavelength of a half. This is not possible because for a closed ended pipe the wave has to end with an anti-node at the open end
What are two ways to increase the frequency in a string
Increasing the tension
Decreasing the length
What does the first harmonic look like for a pipe that is closed on both ends
It should start with a node and end with a node. There should be half a wavelength
How do you find resonance
Move a tube that is closed on one end and open on the other, through water when it is hit with a tuning fork, you will get maximum resonance at each node.
What is phase difference
Where on the wavecycle a point is
