Page 197 - Physics Coursebook 2015 (A level)

Chapter 13: Waves
a
stationary source
b
WORKED EXAMPLE
3
A train with a whistle that emits a note of frequency 800 Hz is approaching an observer at a speed of
60 m s−1. What frequency of note will the observer hear? (Speed of sound in air = 330 m s−1.)
Step1 SelecttheappropriateformoftheDoppler equation. Here the source is approaching the observer so we choose the minus sign:
fo= fs×v (v−vs)
Step2 Substitutevaluesfromthequestionand solve:
fo = 800×330 = 800×330
(330 − 60) 270 = 978 Hz
So the observer hears a note whose pitch is raised significantly, because the train is travelling at a speed which is an appreciable fraction of the speed of sound.
direction of wave travel
v
moving source
vs
Figure 13.12 Sound waves, emitted at constant frequency by a a stationary source, and b a source moving with speed vs away from the observer.
The observed wavelength is now given by λo = (v + vs) . The observed frequency is given by: fs
fo = v = fs×v λo (v + vs)
This tells us how to calculate the observed frequency when the source is moving away from the observer. If the source is moving towards the observer, the train of fs waves will be compressed into a shorter length equal to v − vs, and the observed frequency will be given by:
fo=v= fs×v λo (v−vs)
We can combine these two equations to give a single equation for the Doppler shift in frequency due to a moving source:
observed frequency fo = fs × v (v ± vs)
where the plus sign applies to a receding source and the minus sign to an approaching source. Note these important points:
■■ The frequency fs of the source is not affected by the movement of the source – it still emits fs waves per second.
■■ The speed v of the waves as they travel through the air (or other medium) is also unaffected by the movement of the source.
Note that a Doppler effect can also be heard when an observer is moving relative to a stationary source, and also when both source and observer are moving. There is more about the Doppler effect and light later in this chapter.
QUESTION
10 Aplane’sengineemitsanoteofconstant frequency 120 Hz. It is flying away from an observer at a speed of 80 m s–1. Determine:
a the observed wavelength of the sound received by the observer
b its observed frequency.
(Speed of sound in air = 330 m s−1.)
Electromagnetic waves
You should be familiar with the idea that light is a region of the electromagnetic spectrum. It is not immediately obvious that light has any connection at all with electricity, magnetism and waves. These topics had been the subject
of study by physicists for centuries before the connections between them became apparent.
An electric current always gives rise to a magnetic field (this is known as electromagnetism). A magnetic field is created by any moving charged particles such as electrons. Similarly, a changing magnetic field will induce a current
in a nearby conductor. These observations led to the unification of the theories of electricity and magnetism by Michael Faraday in the mid-19th century. A vast technology based on the theories of electromagnetism developed rapidly, and continues to expand today (Figure 13.13).
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