NATIONAL PUBLIC SCHOOL
ITPL, BENGALURU
INVESTIGATORY PROJECT IN CHEMISTRY
ANALYSIS OF ACIDITY IN FRUITS AND
VEGETABLES
SESSION: 2024-25
CLASS – XI A
Name of the Candidate:
Samartha M 11A
NATIONAL PUBLIC SCHOOL
ITPL, BENGALURU
DEPARTMENT OF PHYSICS
CERTIFICATE
Certified that the work in this file is the bonafide work
of Samartha M grade XI A ,Roll Number 24 recorded
in the school laboratory during the academic year
2023-2024.
Date: 20/08/2024
Teacher in charge External
Examiner School Seal
Acknowledgement
I, Samartha M, would like to express my gratitude to my Physics teacher as well as our Director
Principal Mrs. Vandana Sanjay who gave me the golden opportunity to do this wonderful
project on the topic ‘Doppler Effect’, which has given me a chance to spend time on learning
and exploring something different and intriguing and has great relevance as well. The time
spent on doing the project was indeed worthwhile.
Next, I would like to thank my friends and classmates who were always open to help and clarify
on any issues I came across without hesitation, which truly aided in my progress to complete the
project. Finally, my parents, who were always there to push me and help me with any of my
requirements at any stage of doing the project.
I sincerely thank all.
INDEX
Serial TOPIC Page
No. Number
1. Chapter 1 : Introduction 5
2. Chapter 2 : The Doppler Effect on Sound 6-8
3. Chapter 3 : Wavefronts and their Variation with 9
respect to change in velocity of wave source in terms
of speed of sound
4. Chapter 4 : Doppler Effect in Electromagnetic Waves 10
5. Chapter 5 : Doppler Broadening of Spectral Lines 11
6. Chapter 6 : Receding Galaxies emit Doppler Shifted 12
Light
7. Chapter 7 : Real Life Applications of Doppler Effect 13
8. Chapter 8 : Doppler Spectrography ( A Case Study) 14
9. Chapter 9 : Conclusion 15
10. Bibliography 16
1. INTRODUCTION:
● A real life scenario for proper comprehension of the concept:
You have probably had the experience of hearing an ambulance approaching with its siren blaring, and you
may have noticed that there was a sharp drop in the pitch of the siren as it passed you. That was because,
as it passed you, the siren changed from coming toward you to going away from you. To a person in the
ambulance the siren stayed at a frequency that was between the “coming toward” you (higher) one and
the “going away from” you (lower) one. The single frequency heard by the person in the ambulance was,
in fact, the frequency you would have heard if the ambulance had been stationary. This is true in general:
an approaching source of sound shows a higher frequency than a stationary sound, and a receding source
shows a lower frequency.
● This change in the observed frequency of the sound, due to the motion of the source, is a
consequence of the wave nature of sound and this phenomenon is called the “Doppler effect.” The
change in the observed frequency is called the “Doppler shift.”
● This Doppler effect can be seen for any types of waves like light, waves, water waves. We are mostly
familiar with the Doppler effect of sound in our daily lives.In the world of modern science. Doppler effect
has its application in various fields of science.
2. THE DOPPLER EFFECT FOR SOUND:
Case 1: WHEN BOTH WAVE SOURCE AND RECEIVER ARE STATIONARY:
● Here we review the wavelength-frequency-speed equation for the non-Doppler case, where the sound
wave source and receiver are both at rest with respect to the air (the medium in which the sound
propagates).
● The source produces waves of wavelength λ and frequency ν that travel at wave speed v, the speed of
sound in air. The equation we thus obtain is :
λν = v
[where λ = wavelength, ν = frequency of wave and v = speed of wave]
● Note that in this case the relative velocity between the source and the receiver is 0 and they are at rest with
respect to air.
Case 2 : WHEN THE WAVE SOURCE IS APPROACHING THE RECEIVER:
● Here the wave source is approaching with some velocity say ‘v ᵣ’. Imagine that it travels for the time
period ‘T’ and thus has traversed a distance of v ᵣT. Now it is pretty much evident that the stationary
receiver would observe not wavelength λ but wavelength λ'. This is because of the variation in the velocity
which is relative. The equation now transforms as :
λ' = λ - v ᵣT
● Alteration in wave speed : Surprisingly there is variation in the wave speed
● Once the wave is introduced into the air, its speed is determined by the properties of the medium (density,
elastic response, temperature, etc.) and not by the way the wave was produced. The wave “forgets” its
history, i.e. whether its source was moving or not, hence the wave speed is still v.
ν'λ' = ν'(λ - v ᵣT) = v
Case 3 : WHEN THE RECEIVER IS APPROACHING THE WAVE SOURCE:
● Suppose the receiver is approaching a stationary source with speed vᵣᵥ. Then he would perceive that wave
will more magnitude of speed than usual (velocity of approach)
vᵣₑₗ = v + vᵣᵥ
● The frequency v' perceived by the receiver is determined by this relative speed and the wavelength λ by
the following modified version of the equation :
Case 4 : WHEN BOTH THE WAVE SOURCE AND THE RECEIVER ARE
APPROACHING EACH OTHER:
● By combining the arguments of the previous two situations, the reader should verify that the following
equation must be satisfied for waves emitted by a moving source and perceived by a moving receiver,
approaching one another:
Case 5 : MOTION OF THE WAVE SOURCE IN AN ANGLE:
[C = speed of sound in vacuum, v = velocity of source, θ = angle of motion of source w.r.t the receiver]
● It’s easiest to see what the observed frequency is in this case by looking at the picture .Check that
for θ = 0, this reduces to the ahead case, for θ = π it reduces to the behind case and for θ = π/2 ,
where the observer is orthogonal to the direction, there is no change.
3. WAVEFRONTS AND THEIR VARIATION WITH RESPECT TO VARIATION
OF SPEED OF SOURCE IN TERMS OF SPEED OF SOUND:
● Case 1 : the source has no independent velocity, so it is considered subsonic (less than speed of sound)
● Case 2 : Also considered as subsonic but slight change is seen as a little pressure is generated. The
wavefronts are slowly coming together.
● Case 3 : The source has the speed of sound, at this point it is just generating a sonic boom.
● Case 4 : Sonic boom gets generated (supersonically).
[Note: The large increase in pressure from the accumulation of maxima is followed by a large decrease in
pressure from the minima. This rapid change in pressure is very loud. It is called a sonic boom. ]
4. DOPPLER EFFECT IN ELECTROMAGNETIC WAVES :
● The Doppler effect in electromagnetic waves refers to the change in frequency (and consequently
wavelength) of electromagnetic waves, such as light, due to the relative motion between the source of the
waves and the observer. This phenomenon is similar to the Doppler effect observed with sound waves but
applies to all types of electromagnetic radiation, including visible light, radio waves, and X-rays.
● Other related phenomenon observed :
1. REDSHIFT : If the source of electromagnetic waves is moving away from the observer, the
observed frequency decreases, leading to a shift towards the red end of the spectrum (longer
wavelengths). This is called redshift.
2. BLUESHIFT : If the source is moving towards the observer, the observed frequency increases,
resulting in a shift towards the blue end of the spectrum (shorter wavelengths). This is known as
blueshift.
5. DOPPLER BROADENING OF SPECTRAL LINES :
● An important example of the Doppler effect for light is the “broadening” of spectral lines due to the
thermal motion of the atomic or molecular sources of light.
● These sources emit or absorb electromagnetic radiation in a spectrum of discrete frequencies called
“spectral lines.” Each spectral “line” may be represented on a graph of radiation intensity as a function of
frequency.
● The spectral line has a peak at some frequency νₒ and a “width” measured at half the peak intensity. This
width has a minimum value called the “natural line width,” representing the fact that frequencies other
than νₒ may be emitted or absorbed, although such frequencies occur with lower intensities
● However, since the atomic or molecular sources are in random thermal motion with a Gaussian distribution
of velocities, the observed frequencies are a similar distribution about the peak frequency νₒ. This effect is
called the “broadening” of the spectral line (beyond its “ natural” width). Such a spectral “line” has a width
of roughly 2∆ν, where ∆ν is the Doppler shift for a source moving at the average speed of the thermal
distribution
6. RECEDING GALAXIES EMIT DOPPLER SHIFTED LIGHT:
● One of the most important pieces of evidence supporting the expanding universe model is the
Doppler shift of spectral line frequencies of light emitted from stars in distant galaxies. These
spectral lines are easily identified by comparison with laboratory spectra, but are consistently
shifted to lower frequencies. Such shifts, called “red shifts,” indicate that the star as a whole is
receding from the earth
● No such stellar spectra have been observed to be Doppler shifted to higher frequencies
(“blue-shifted”), leading to the inescapable conclusion that the galaxies are receding from each
other and that the universe is expanding.
7. REAL LIFE APPLICATIONS OF DOPPLER EFFECT
1. Astronomy: The Doppler Effect is crucial in studying the motion of celestial bodies. By analyzing the
redshift or blueshift of light from stars and galaxies, astronomers can determine their velocity relative to
Earth. This information is essential in understanding the universe's expansion, measuring the speed of
stars, and detecting exoplanets through the wobble of their host stars.
2. Radar and Sonar: The Doppler Effect is fundamental to radar and sonar technology, where it helps
determine the speed and direction of objects. For example, police radar guns use the Doppler Effect to
measure a vehicle's speed, and sonar systems utilize it to detect submarines or underwater objects.
3. Medical Imaging: In medicine, Doppler ultrasound is used to measure blood flow in arteries and veins,
detecting blockages and abnormalities. The Doppler Effect allows clinicians to visualize blood flow
patterns and diagnose cardiovascular conditions.
4. Meteorology: Weather radar systems use the Doppler Effect to measure the velocity of precipitation
particles, helping meteorologists predict severe weather events like tornadoes and thunderstorms.
5. Vibration Measurement: Done using Doppler vibrometer. It generates a laser beam which moves towards
the object's surface.
6. Military: Helps to identify submarine speed. Generates consistent and stable frequencies.
8. DOPPLER SPECTROSCOPY (A Case Study):
● Gasses in stars emit and absorb light at specific frequencies, corresponding to transition energies between
electron orbitals.
● The spectrum of a star therefore contains many narrow peaks and troughs, called spectral lines.
● If the star is moving relative to our telescope, then its entire spectrum is either redshifted or blueshifted.
● The redshift of a star can therefore be determined very precisely by measuring the offset of certain spectral
lines from their standard frequencies.
● This method, called Doppler spectroscopy, allows a precise measurement of the velocity of a star along the
line of sight. This velocity is called the radial velocity of the star.
● Here is an example of the motion of a star (51 Pegasi) determined from Doppler spectroscopy:
Observations and Inferences :
● We see that there is a periodic oscillation of the velocity.
● This can be explained if there is a planet orbiting the star.
● For example, imagine some alien is looking at the earth from far away. The average velocity of the earth is
the average velocity of our solar system.
● But when the earth is on one side of the sun, it moves away from the alien and on the other side, it moves
towards the alien.
● Thus the earth’s velocity as viewed from far away has wiggles due to the annual orbit.
● If the earth were much bigger, the sun would also have detectable wiggles. So what we are seeing in the 51
Pegasi spectrum above are wiggles due to a very large planet in a tight orbit with that star.
9. CONCLUSION
● Experience shows that the assumptions about wave motion on which our Doppler shift results were
derived are not always valid.
● One limitation to the Doppler shift equations arises from the assumption that the speed of the source is less
than the speed of the wave. However, if the receiver is receding from the source at a speed exceeding the
wave speed, the wave will never catch up and hence will never be observed at all.
● The Doppler Effect is a cornerstone concept in wave physics, with diverse applications across science and
technology. Whether it's hearing the pitch change of a passing siren or measuring the expansion of the
universe, the Doppler Effect provides critical insights into the relative motion between sources and
observers.
● The mathematical principles underlying the Doppler Effect, though varying for different wave types, offer
a quantitative framework for understanding how wave frequencies shift due to movement.
● By mastering these concepts, scientists and engineers can continue to unlock new knowledge and develop
innovative technologies in fields ranging from astronomy to medicine.
10. BIBLIOGRAPHY :
1. THE DOPPLER EFFECT by Mary Lu Larsen Towson State University
2. https://www.physnet.org
3. Lecture 21: The Doppler effect by Matthew Schwartz
4. Wikipedia.com
5. https://www.jpl.nasa.gov/
6. https://www.webassign.net/
