Option A: Sight and Wave Phenomena IB Physics Doppler Effect Option A: Sight and Wave Phenomena IB Physics

10.1.1 Describe and Explain the Doppler Effect The Doppler effect, named after Christian Doppler, is the change in frequency and wavelength of a wave as perceived by an observer moving relative to the source of the waves. For waves that propagate in a wave medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted.

The total Doppler effect may therefore result from motion of the source or motion of the observer or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as light or gravity in special relativity, only the relative difference in velocity between the observer and the source needs to be considered. Video – Doppler effect and train.

Doppler and Light

10.1.2 Wavefront Diagrams – Moving Source

Moving Source - receding

Equation – moving source f ’ = f __v__ v + us Where f ‘ = frequency observed by the stationary observer in Hz f = frequency of source v = speed of sound us = speed of emitting source + = source moving away from the observer - = source moving towards observer

Simplifying the equation f ’ = f __v__ v + us Multiply throughout by v gives f ’ = f __1__ 1 + us v Where + = moving away from the observer - = moving towards the observer v = speed of sound in medium us = speed of the source

Your Task Draw wavefront diagrams if you were moving and the source was staying still.

Moving Observer What happens when the observer is moving towards the source? Base equation from IB Physics data book f ‘ = f v ± uo v Multiply throughout by v gives Observer moving towards source f’ = f 1 + uo Observer moving away from source f’ = f 1 - uo

Examples See text p 299 for a worked example and the do Exercise about ‘Judy on the platform of a station’

Doppler Effect and Light The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blue shift. It has been used to measure the speed at which stars and galaxies are approaching or receding from us, that is, the radial velocity. This is used to detect if an apparently single star is, in reality, a close binary and even to measure the rotational speed of stars and galaxies.

Red and Blue Shift - Doppler

Doppler Applications Police use this property in the radar boxes they use to track speed. Radio waves are transmitted out, collide with a vehicle, and bounce back. The speed of the vehicle (which acts as the source of the reflected wave) determines the change in frequency, which can be detected with the box. (Similar applications can be used to measure wind velocities in the atmosphere, which is the "Doppler radar" of which meteorologists are so fond.)

Echocardiograms - Doppler An echocardiogram can, within certain limits, produce accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, any abnormal communications between the left and right side of the heart, any leaking of blood through the valves (valvular regurgitation), and calculation of the cardiac output.

This Doppler shift is also used to track satellites. By observing how the frequency changes, you can determine the velocity relative to your location, which allows ground-based tracking to analyze the movement of objects in space.

In astronomy, these shifts prove helpful. When observing a system with two stars, you can tell which is moving toward you and which away by analyzing how the frequencies change.

Even more significantly, evidence from the analysis of light from distant galaxies shows that the light experiences a red shift. These galaxies are moving away from the Earth. In fact, the results of this are a bit beyond the mere Doppler effect. This is actually a result of spacetime itself expanding, as predicted by general relativity. Extrapolations of this evidence, along with other findings, support the "big bang" picture of the origin of the universe.

A question for you to do! A source of sound emits waves of wavelength λ, period T and speed v when at rest. The source moves away from a stationary observer at speed V, relative to the observer. The wavelength of the sound waves, as measured by the observer is A. λ + vT. B. λ – vT. C. λ +VT. D. λ – VT. Answer C

10.2 Beats Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another. The diagram below illustrates the wave interference pattern resulting from two waves (drawn in red and blue) with very similar frequencies. A beat pattern is characterized by a wave whose amplitude is changing at a regular rate.

Observe that the beat pattern (drawn in green) repeatedly oscillates from zero amplitude to a large amplitude, back to zero amplitude throughout the pattern. Points of constructive interference (C.I.) and destructive interference (D.I.) are labelled on the diagram. When constructive interference occurs between two crests or two troughs, a loud sound is heard. This corresponds to a peak on the beat pattern (drawn in green).

When destructive interference between a crest and a trough occurs, no sound is heard; this corresponds to a point of no displacement on the beat pattern. Since there is a clear relationship between the amplitude and the loudness, this beat pattern would be consistent with a wave which varies in volume at a regular rate.

Beat Frequency The beat frequency refers to the rate at which the volume is heard to be oscillating from high to low volume. For example, if two complete cycles of high and low volumes are heard every second, the beat frequency is 2 Hz. The beat frequency is always equal to the difference in frequency of the two notes which interfere to produce the beats. So if two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a beat frequency of 2 Hz will be detected.

When you superimpose two sine waves of different frequencies, you get components at the sum and difference of the two frequencies. This can be shown by using a sum rule from trigonometry. For equal amplitude sine waves

Superposition Relationship

The first term gives the phenomenon of beats with a beat frequency equal to the difference between the frequencies mixed. The beat frequency is given by

Wave interference is a phenomenon which occurs when two waves meet while travelling along the same medium. Wave interference can be constructive or destructive. The interference of two sets of circular waves with the same frequency and the same amplitude results in a standing wave pattern. These standing wave patterns are known as two-point source interference patterns since they result from the interference of circular waves from two sources. A standing wave pattern is a wave pattern in which there are points along the medium which appear to be standing still. These points are called nodes - points of no displacement.

Nodes are produced when destructive interference always occurs at the same location. Both waves have the same magnitude of displacement in opposite directions and interfere to provide complete destructive interference and no resulting displacement of the medium. In a standing wave pattern, the nodes are separated by antinodes. Antinodes are points along the medium which oscillate between a large negative displacement and a large positive displacement. Antinodes result from the constructive interference of two waves. At the antinodal positions, a crest meets a crest to produce a large positive displacement. Moments later, a trough meets a trough to produce a large negative displacement.

Nodal Lines The diagram below shows several two-point source interference patterns. T he crests of each wave is denoted by a thick line while the troughs are denoted by a thin line. Subsequently, the antinodes are the points where either the thick lines are meeting or the thin lines are meeting. The nodes are the points where a thick line meets a thin line.

Observe that the nodes of the pattern are oriented along lines - known as nodal lines. Similarly, the anti-nodes in the pattern are also oriented along lines - known as antinodal lines. The spacing between these lines is related to the wavelength of the light. As the wavelength increases, the spacing between the nodal lines and the anti-nodal lines increases. That is, the nodal and antinodal lines spread farther apart as the wavelength gets larger.

In 1801, Thomas Young used a two-point source interference pattern to measure the wavelength of light. Young passed sunlight through two slits (acting as the sources) and upon a screen some distance away. The projection of the nodal and anti-nodal lines on the screen produced an alternating pattern of dark and bright lines. Young used wave principles to establish that the wavelength of light could be mathematically related to the separation distance, the distance to the screen, and the distance between anti-nodal lines (bright spots). Young made accurate measurements and determined the wavelength of light.