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Physics - The Wave Equation (AQA Syllabus A)

Electromagnetic and mechanical waves are both studied in GCSE Science. This is the fourth of six quizzes on waves and it looks at the wave equation, which describes the relationship between velocity, frequency and wavelength.

There are two types of wave - transverse and longitudinal. Each has its own properties but all waves have one thing in common - they obey the wave equation. This shows how the speed of the wave is related to the frequency and the wavelength, and knowing any two of them can be used to calculate the missing value. It allows you to predict what effect making any changes will have on the wave. The wave equation is:

v = fλ, using the scientific symbols, or speed of the wave = frequency of the wave x wavelength of the wave in plain English.

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Before you use the equation it does help to know a little more about the three terms. The speed of the wave can be in a variety of units, the official SI unit is metres per second which is written as m/s or ms-1. This is the most likely unit that will be used in your exams but every now and then the examiners might throw in some different units just to check how you handle them. Being picky, the speed of a wave is a velocity since waves travel in straight lines. Using the term wave speed rather than wave velocity covers situations where the wave changes direction by reflection, refraction and diffraction. That information is a little extra, just for you - you don't need to know it for the exams.

The wavelength of the wave is the distance from one point on a wave to the equivalent point on the next wave. On diagrams of waves it is usually shown as being from crest to crest (make sure you learn the different parts of a wave for the exams). For a longitudinal wave the definition is the same but instead of a crest they have compressions. So a sound wave with a wavelength of 2 m will have a compression every 2 metres along its length. The number of waves passing a given point in one second is the frequency.

Many of the questions you will be asked about waves will concern the electromagnetic spectrum - the family of waves that include radio waves and light waves. You don't need to know the actual wavelengths and frequencies for each one but you do need to know the names of the waves in order of wavelength and frequency, the approximate shortest and longest wavelengths/frequencies and the fact they all travel at the same speed.

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  1. Wave frequency is measured in which unit?
    One Hz = one wave passing per second. Gauss are the units of magnetism and wave-seconds don't exist
  2. A keyboard player plays a note of 440 Hz. What does this mean?
    The normal range of human hearing is 20 Hz to 20 kHz. The frequency tells you how many waves reach a given point (or go past an observer) in a second
  3. If a wave of 440 Hz travels at 340 m/s, what is its wavelength?
    You need to rearrange the wave equation to ë = v/f
  4. What is the wavelength of the microwaves used by a mobile phone operator that uses microwaves with a frequency of 1.8 x 109 Hz and which travel at a speed of 3.0 x 108 m/s to transmit their signals?
    Working with powers of ten can be tricky. Make sure you do a rough calculation using the powers of ten so that you know if your final answer is in the right area
  5. Electromagnetic waves travel through space at a speed of 3.0 x 108 m/s. The radio waves emitted from a distant galaxy have a wavelength of 25 metres. What is the frequency of the radio waves emitted from the galaxy?
    The difference between the last two answers is the units - mhz is wrong because the capitalisation is incorrect. As well as checking that you can rearrange the wave equation, it tests if you are aware of the correct way to write units
  6. Electromagnetic waves travel at a speed of 3.0 x 108 m/s through the air. A radio station transmits using waves with a wavelength of 1.9 x 102 m. At what frequency would you need to set your radio to receive this particular station's programmes?
    Did you get the rearranged equation the correct way up?
  7. A group of students carried out an experiment using a ripple tank. They measured the frequency of a wave as being 14 Hz with a total of 20 wave crests in the tank. The tank was 40 cm long. How fast was the wave travelling?
    When dealing with complex questions like this, you need to break them down into smaller steps. To do that, start from the equation you need to work out the speed v = fë. You have the frequency and need the wavelength. So you then look at the other information to see how you can work out the wavelength from the data. Once you have that, it is a simple matter of plugging the figures into the equation
  8. What is the wavelength of the musical note middle C? It has a frequency 256 Hz and the speed of sound is 335 m/s.
    You will see various different values for the speed of sound because it varies according to the air pressure
  9. Waves are diffracted when they pass through a gap that is about the same width as their wavelength. What width of gap would be required to cause microwaves of frequency 1.5 x 1010 Hz to diffract?
    This is a wavelength question, but slightly disguised! We didn't give you the speed of the waves because, by now, you should know that microwaves travel at the same speed as all electromagnetic waves - 3 x 108 m/s. That is actually the speed they travel in a vacuum but it isn't much different in other media
  10. Snakes swim by vibrating their body from side to side, just like a transverse wave. The faster they vibrate, the faster they move through the water. A 90 cm long snake in a lake travels with a velocity of 1.8 m/s. At what frequency does it vibrate its body?
    A nice easy finish for you, hopefully you did this one using mental arithmetic - 1.8 (m/s) divided by 0.9 (m). Mental arithmetic can save time in the exams but is not always possible

Author: Kev Woodward

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