Definition: a change in the wavelength and frequency of a wave caused by relative movement of the wave source and the observer.
This occurs in all waves → sound, electromagnetic, etc.
When the source of a wave is moving relative to the obeserver it means that the waves produced are compressed, as shown in the diagram, if the source is moving towards you.
This means that the wavelength has decreased.
As the speed of the wave remains the same, the frequency has to increase.
We know this by looking at the equation for wave speed:
v = f x λ
Remember, this only occurs if the source is moving at a different speed to the observer. If they are moving at the same speed, the effect doesn’t occur.
So, because the frequency appears to have increased, the sound is higher pitched.
If the source was moving away, the wavelength would be longer, so frequency would be smaller, meaning the sound would be lower pitched.
This effect is exhibited best when a siren drives past you; the pitch appears to change depending on how far away from you the siren is, and whether is is coming towards you or moving away.
Red and Blue Shift
Red Shift Definition: The increase in wavelength and so decrease in frequency of electromagnetic radiation from distant, receding galaxies due to the Doppler effect and the expansion of the Universe.
So, essentially, this is the Doppler effect, but with light or other electromagnetic radiation. In the same way sound appears more high pitched when the source moves towards us, light appears more “blue” when it is moving towards us, and more “red” when it is moving away.
Red Shift as Evidence of the Big Bang
The big bang theory states that a huge explosion occured about 13.7 billion years ago that released so much energy that energy became matter, and the universe was born. It also states that the universe continues to expand to this day.
We can use red shift as evidence for this. This is because when electromagnetic waves move away from us, they are red shifted as their wavelength appears longer. The light we see from stars across the universe is red shifted; this means they are moving away from us. Since they are moving away, it indicates that the universe is expanding, as if it was staying the same, the light would exhibit no red or blue shift.
For example, if 3 objects were floating in a balloon, and that balloon was inflated more, then the volume of the balloon would expand, and the objects would move further apart.
Also, the more red shifted a star is, the further away from us it is. So we can use the amount of red shift a star exhibits to find out how far away it is from us.
Definition: a system that transmits a force from one place to another through a fluid.
Hydraulic systems are classed as force multipliers.
For this topic, it’s important to remember about pressure in liquids → they are incompressible.
An example of a hydraulic system is in car brakes (please spell it brakes, not breaks).
Hydraulic systems are useful because they essentially convert a small force on a small area to a large force on a large area, meaning people are able to exert a huge force on a massive object, such as breaks in a car.
To see how they do this, we look at the idea of pressure.
Here is a diagram of a hydraulic system:
Now, we know that pressure is equal to force divided by area (shown below).
And due to liquids being incompressible, the pressure is equal throughout the whole liquid – it remains constant. This is why it is an issue when break fluid leaks in cars, as the pressure is not transferred through the liquid, and so the force exerted on the break pads is not transferred to the whole vehicle.
So if the pressure exerted by the small force on the small area is equal to the pressure transmitted by the liquid to the large area, we can conclude:
The pressure is the same as that exerted by the small force on the small surface area. The surface area is bigger. This means that the force is bigger too, due to the equation for pressure rearranging like this:
I know this is difficult to get your heads round, but to summarise:
A small force is exerted on a small surface area → this results in a pressure → this pressure remains constant as it is transmitted through an incompressible liquid to a larger surface area → the pressure is being exerted on a surface area which is larger than the first one → due to the equation force = pressure x area, the force exerted on the second surface is larger than the force exerted on the first.
Since it’s quite complicated, here’s an example question:
A force of 30N is applied to piston A with a surface area of 0.2m² in a hydraulic system.
The surface area of piston B is 1.0m².
What is the force exerted by piston B?
So, the pressure exerted on piston A is force/area : 30N divided by 0.2m² is 150Pa.
To find the force exerted by piston B, we rearrange the equation to get pressure x area. So 150Pa x 1 m² = 150N.
Definition: the force exerted divided by the area on which it is exerted → measured in Pascals (Pa).
We know that force is measured in Newtons, and area is measured in metres squared. So pressure is measured in newtons per metre squared. This is a unit called Pascals.
We can use the equations to conclude that a wider area means there is less force exerted per metre squared → a wider area = less pressure. This provides an explanation as to why flat shoes don’t sink as easily in mud as highheels.
The atmospheric pressure on earth is 100 000 Pa.
Pressure in Liquids
We describe liquids as being virtually incompressible. This is because there are no gaps and no space between the liquid molecules.
The pressure exerted by the liquid (shown in red) is the same in all directions.
[as year 11s I am sure you are familiar with the sensation of pressure. you’ll be fine]
For example, a playground swing, with the mass being the person on the seat.
How it works: The swing of a pendulum can be described by its:
amplitude → how far from the vertical (the dotted line on the diagram) the string moves.
time period → time taken for one complete swing.
frequency → number of complete swings per second.
When a pendulum is swinging we say it is oscillating.
The time period is directly proportional to the square root of the length of the string:
The frequency of the oscillations is equal to 1 divided by the time period:
T = time period → unit: seconds (s)
f = frequency → unit: Hertz (Hz)
L = length → unit: metres (m) examiners often trip students up by using cm or mm. Ensure you have converted all units before beginning your calculations.
We can conclude by looking at the equations that:
the longer the pendulum → the longer the time period → the smaller the frequency
The time period of a pendulum can be affected by:
mass of the bob
length of the string
Definition: an unpredictable variation around the true value, causing each reading to be slightly different.
So, basically, mistakes. These are often human errors. One very common, and unavoidable, human error is the reaction time error.
As you know, it takes us a moment to react, for example, there will be some time between releasing the pendulum to swing and starting the stopwatch.
This is on average 0.2 seconds in humans.
To reduce the impact of this reaction time on results, record the time it takes for several oscillations to occur, such as 10 or 15, and then find the average. This will make reaction time almost negligible.