Astrophysics >>
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Waves are incredibly important in nature. They are periodic and repetitive disturbances of a medium, which can be used to transmit energy and/or information. We live in a Universe full of wave phenomena: light, sound and water waves being the most obvious. In this unit we look at how these three forms of waves behave and look at how their frequency, amplitude, speed and direction can all be changed - and can be made to fool our senses.
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June 2018 - My wife was hired to perform at a wedding at the lovely Reefs Hotel. As I was relaxing at the bar and admiring the view on what was a lovely afternoon, I started thing about all the waves that were in evidence.
Slide to expose what the physicist 'sees'! |
4.1 - General Properties of Waves
- Describe longitudinal and transverse waves in ropes; springs and water where appropriate state the meaning of amplitude, frequency, wavelength and period of a wave.
- Recall that waves transfer energy and information without transferring matter use the relationship between frequency and time period.
- Use the above relationships in different contexts including sound waves and electromagnetic waves.
Waves are caused by a vibration and radiate outwards from their source. You have to know the two types of waves, their parts and how they interrelate. Ocean waves and light are transverse (vibration is perpendicular to the direction of the wave) and sound is longitudinal (vibration is parallel to the direction of travel)
Animation of a longitudinal wave (i.e. sound). Note that as above the medium as a whole does not move, but each particle vibrates left and right.
Both of these excellent animations come from Pennsylvania State University: http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html |
Wavelength - distance between any two successive waves, usually best remembered as the distance between two peaks. Unit is usually metres (m), but can be any derivative of this (cm, mm, km etc)
Frequency - number of complete waves per second. Unit is hertz (Hz) Period - the time taken to complete one waves. Unit is seconds (s). Note that the period and frequency are different ways of saying the same thing - i.e. the rate of vibration of the wave. Wave velocity - how fast the wave moves. Unit is usually metres/second (m/s) but can be others. Amplitude - how high the wave is. This is measured from the undisturbed level to the peak. |
\[f=\frac{1}{T}\]
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This equation is fundamental. It relates the frequency to the period - essentially the same concept. Learn it!
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\[v=f\lambda\]
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This is the wave equation that links velocity, frequency and wavelength. It is based on the simple equation speed = distance/time. It is frequently used in this topic, especially with electromagnetic waves questions.
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4.2 - Sound Waves
- Recall that sound waves are longitudinal waves which can be reflected, refracted and diffracted.
- Recall that the frequency range for human hearing is \(20 \,\text{Hz} \rightarrow 20,000 \,\text{Hz}\).
- Appreciate that the loudness of a sound depends on the amplitude of vibration.
- Describe how to measure the speed of sound in air by a simple direct method.
- Understand how an oscilloscope and microphone can be used to display a sound wave.
- Use an oscilloscope to determine the frequency of a sound wave and appreciate that the pitch of a sound depends on the frequency of vibration.
Sound is caused by a vibration of something and is carried as a vibration through a medium (solid, liquid or gas). We hear it with our ears and young students can hear frequencies ranging from \(20 \,\text{Hz}\) to \(20,000 \,\text{Hz}\). Sound vibrations above that frequency cannot be heard and are known as ultrasound. Sound wave that reflect off a surface are called echoes. The speed of sound varies a lot and is partly dependent on the density of the medium.
Sound waves can only travel as fast the molecules of that medium can pass on the vibration from one molecule to the next. The denser the medium, the faster they can travel. As a vacuum contains nothing, sound cannot travel through it. This was demonstrated in the class by a bell inside a jar with the air pumped out. When an object is pushed through air faster than the speed of sound a shock wave is created. The two most famous examples are: supersonic aircraft and thunder. Chuck Yeager was the first man to break the sound barrier.
Sound waves can only travel as fast the molecules of that medium can pass on the vibration from one molecule to the next. The denser the medium, the faster they can travel. As a vacuum contains nothing, sound cannot travel through it. This was demonstrated in the class by a bell inside a jar with the air pumped out. When an object is pushed through air faster than the speed of sound a shock wave is created. The two most famous examples are: supersonic aircraft and thunder. Chuck Yeager was the first man to break the sound barrier.
Medium |
Speed of Sound (m/s) |
Air |
330 - 340 |
Water |
1500 |
Steel |
5000 |
Vacuum |
0 |
LAB - Measuring the Speed of Sound
There are several method to measure the speed of sound in air - this is the most consistently accurate.
Two microphones are set up at a distance and connected to a fast timer (such as a scalar timer). One microphone will trigger the timer to start, and the other to stop. The timer needs to be accurate to at least 0.1 ms. A loud, firm tap of metal on metal in front of the first microphone will work. Record the distance and divide by the time on the timer (remembering to convert to seconds). Repeat at least three times. For improved accuracy, repeat over a large range of distances and plot a graph - the gradient of the line-of-best-fit will yield the speed of sound. Note that the microphones must be above the table top!
Sample results: distance = 1.373 m, mean time = 4.093 ms.
\[s=\frac{d}{t}\]
\[s=\frac{1.373}{4.093\,\times\,10^{-3}}\]
\[s=335\,\text{m/s}\]
Which is right between the textbook range of 330 - 340 m/s! wow
Sample results: distance = 1.373 m, mean time = 4.093 ms.
\[s=\frac{d}{t}\]
\[s=\frac{1.373}{4.093\,\times\,10^{-3}}\]
\[s=335\,\text{m/s}\]
Which is right between the textbook range of 330 - 340 m/s! wow
Sound waves are longitudinal pressure waves and cannot generally be seen. It is possible to visualise them though. The oldest method is to hook a microphone up to an oscilloscope. The microphone converts physical vibrations into electrical signals and the oscilloscope records how the voltages produced vary with time. Essentially the oscilloscope screen shows a graph of microphone voltage (amplitude) as a function of time. We no longer have a functioning oscilloscope, but luckily developers have produced programs and apps that use the microphone built into a laptop or phone. Not as useful, but they get the job done! Here is a screenshot from the best windows version that I have found. Soundcard Scope
From the screen, the period is 2.5 ms. Remember to convert to seconds.
\[f=\frac{1}{T}\] \[f = \frac{1}{2.5\,\times\,10^{-3}}\] \[f=400\,\text{Hz}\] (which is the frequency that I set the online tone generator to) |
ACTIVITY - use this oscilloscope (or other versions) to see how the wave changes if you a) change the volume (loudness) of the sound wave and b) change the pitch of the sound wave. Try with both your voice and the online tone generator.
Extension - if sound waves cause an object to vibrate at the frequency that it naturally wants to vibrate at we get a phenomenon known as resonance. This is the principle behind the wooden box under the strings in cellos and guitars. The air inside the box resonates and the amplitude of the vibration dramatically increases. Pushing this to its limit it is possible to use sound waves to break things - the opera singer's wine glass trick is the classic case. the frequency that a good quality wine glass wants to oscillate at (its natural frequency) can be found by dampening your finger and running it around the edge. If this frequency can then be matched by an external sound, it is possible to break the glass.
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4.3 - The Wave Equation
- Recall and use the relationship between the speed, frequency and wavelength of a wave:
- wave speed = frequency × wavelength. \(v = f\lambda\)
The so-called wave equation is a very useful way of converting between wavelength and frequency. It is derived from the very simple relationship of speed = distance/time, but let the distance for one time period equal the wavelength, so the equation changes to:
\[v = \frac{x}{t}=\frac{\lambda }{T}\]
\[v = \frac{x}{t}=\frac{\lambda }{T}\]
Then, because the frequency is the reciprocal of the period, we get the useful form of the equation:
\[v = f\lambda\]
\[v = f\lambda\]
4.4 - The Electromagnetic Spectrum
- Understand that light is part of a continuous electromagnetic spectrum.
- Recall the order of the EM spectrum – including the visible colours.
- Recall the uses of the various EM radiations.
- Recall the dangers of high frequency EM waves.
Electromagnetic (EM) waves are made up from vibrating electric and magnetic fields. They are all transverse and travel at the same speed, the speed of light. Some of these waves will be very familiar to you. The most obvious is the LIGHT that we see! You have already met Infrared (IR) as thermal radiation and in Bermuda we all know about the dangers of ultra-violet (UV) radiation from the Sun, that caused sunburn and skin cancer. (Quick reminder: Slip, slap, slop!) The different properties between groups of them is purely due to the vastly different frequencies. The energy carried by the wave is proportional to the frequency of the wave. The really high frequency waves, such as X-rays and gamma rays, carry huge amounts of energy and are extremely hazardous to biological life. UV is less hazardous but can cause long term damage (blindness and skin cancer). At IGCSE you are expected to know the different properties and used of the various groups of waves, know their speed and be able to calculate the period, frequency and wavelength. For this you MUST be able to use standard form.
\[c = 3 \times 10^{8}\text{m/s}\]
\[c = 3 \times 10^{8}\text{m/s}\]
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Sunscreen and UV light. The sunny days in Bermuda can be brutal on the skin. A suntan can quickly turn into a painful sunburn after a relatively short time. If frequently exposed, the skin can become permanently damaged or even cancerous.
The rule that we all know is of course - SLIP, SLAP, SLOP.
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4.5 - Reflection
- recall that light waves are transverse waves which can be reflected.
- recall that the angle of incidence equals the angle of reflection.
- construct ray diagrams to illustrate the formation of a virtual image in a plane mirror.
Light travels a ray - we draw them as straight lines with arrows to indicate the direction of travel. They travel in straight lines unless something happens at a boundary of something.
When a ray of light strikes a plane (flat) mirror the angle it is reflected at is equal to the angle that it came in. The only complication is that we measure the angles from a reference line called a normal. The normal is perpendicular to the surface of the mirror at the point where the light strikes.
Images are formed behind the mirror as the brain 'believes' that light has traveled in a straight line and has come from the image rather than the object itself!
Curved mirrors are common and very cool!
- Reflection - the light bounces off a surface (e.g. mirror)
- Refraction - the light bends as it goes from one transparent medium to another
- Dispersion - white light bends and splits into different colours as it goes through a prism
- Diffraction - the light spreads out as it goes through a tiny gap (not really covered at IGCSE)
- Interference - light interferes with itself as it goes through two or more gaps (not covered at all in IGCSE)
When a ray of light strikes a plane (flat) mirror the angle it is reflected at is equal to the angle that it came in. The only complication is that we measure the angles from a reference line called a normal. The normal is perpendicular to the surface of the mirror at the point where the light strikes.
Images are formed behind the mirror as the brain 'believes' that light has traveled in a straight line and has come from the image rather than the object itself!
Curved mirrors are common and very cool!
4.6 - Refraction
- describe experiments to investigate the refraction of light, using rectangular blocks, semicircular blocks and triangular prisms.
- recall and use the relationship between refractive index, angle of incidence and angle of refraction
When light travels from one transparent medium to another its speed changes. For example, when light is going through a vacuum it is moving at \(3.0\,\times\,10^8\,\text{m/s}\), and it slows by a third to \(2.0\,\times\,10^8\,\text{m/s}\) when it hits glass. You can imagine that this is caused by the greater density of glass, the factor that it is slowed by is known as the refractive index. The difference in the speed of light in air to that in a vacuum is tiny and at IGCSE/AP we usually ignore it.
The consequence of this sudden change of speed is that the light ray bends at the interface between the media. (See the AP Physics 2 Optics section for a detailed reason why.) The amount of bending depends on two variables: the angle of the incoming (incident) ray of light and the refractive index, \(n\), of the medium.
LAB work - you will be aiming a ray of light from a raybox into a semi-circular plastic block at a range of angles and recording the angle that it is refracted by. The data will not be proportional, but rather curved. The relationship is called Snell's Law and is:
\[n=\frac{\sin{i}}{\sin{r}}\]
So to produce a linear graph to show this you will need to calculate the sines of the angles and plot these.
The consequence of this sudden change of speed is that the light ray bends at the interface between the media. (See the AP Physics 2 Optics section for a detailed reason why.) The amount of bending depends on two variables: the angle of the incoming (incident) ray of light and the refractive index, \(n\), of the medium.
LAB work - you will be aiming a ray of light from a raybox into a semi-circular plastic block at a range of angles and recording the angle that it is refracted by. The data will not be proportional, but rather curved. The relationship is called Snell's Law and is:
\[n=\frac{\sin{i}}{\sin{r}}\]
So to produce a linear graph to show this you will need to calculate the sines of the angles and plot these.
PhET Bending Light - this is the best simulation there is to get the hang of how refraction works. It does have the partial reflection which is not examined, which is why glass can sometimes act as a mirror. You can ignore this.
Taking it further: you can use the prisms section to try to figure out how lenses work. A simple lens is a glass square with a prism at the top and bottom of it. |
4.7 - Total Internal Reflection
- recall the meaning of critical angle \(c\)
- recall and use the relationship between critical angle and refractive index:
When light passes from a more dense medium (say glass) to a less dense one (air), it speeds up. This causes it to refract away from the normal. As the angle of refraction is greater than the angle of incidence, it is possible that the angle of refraction can reach 90 degrees. In which case it will no longer travel out of the glass, but rather be trapped within it. It refects off the surface. There is always some light reflected off an interface (partial reflection), but this will be all of the light. The internal reflection is total. The angle of incidence where this occurs is known as the critical angle. This occurs often in everyday life. If a watch or scuba face mask is looked at underwater at the right angle it appears to turn silver - like a mirror.
4.8 - Communication Systems
- Describe the role of total internal reflection in transmitting information along optical fibres and in prisms.
- Understand the difference between analogue and digital signals.