25Doppler's effect and Musical sound

📚
DOPPLER EFFECT AND MUSICAL SOUND
▢ Doppler Effect:
❖ Definition: Apparent change in frequency of sound heard by observer due to relative motion between source, observer and medium
❖ Shown By:
  • •
    Sound waves
  • •
    Light waves
  • •
    Electromagnetic waves
❖ Nature:
  • •
    Sound Doppler effect is not symmetrical
  • •
    Light Doppler effect is symmetrical
  • •
    Sound Doppler effect does not occur in transverse direction
  • •
    Light can show transverse Doppler effect
  • •
    Apparent frequency increases when source and observer approach
  • •
    Apparent frequency decreases when source and observer recede
❖ Key Concept:

Table 1: Effect of Motion

Motion
Change
Source motion
Changes apparent wavelength
Observer motion
Changes apparent frequency
Same speed same direction
No Doppler effect
Mutually perpendicular motion
No Doppler effect for sound
Only medium moves
No Doppler effect
Circular motion with constant distance
No Doppler effect
▢ General Doppler Formula for Sound:

Table 1: Symbols

Symbol
Meaning
n
Original frequency of source
n'
Apparent frequency
v
Velocity of sound in air
v_o
Velocity of observer
v_s
Velocity of source

Table 2: Formula

Case
Formula
General
\(n'=\frac{v\pm v_o}{v\mp v_s}\times n\)
Source and observer approaching
\(n'=\frac{v+v_o}{v-v_s}\times n\)
Source and observer receding
\(n'=\frac{v-v_o}{v+v_s}\times n\)
Observer towards source
\(+v_o\)
Observer away from source
\(-v_o\)
Source towards observer
\(-v_s\) in denominator
Source away from observer
\(+v_s\) in denominator
▢ Source Passing Listener:

Table 1: Frequency Jump

Case
Formula
Source passes stationary listener
\(\Delta n=\frac{2v_s}{v-v_s}n\)
If \(v_s\ll v\)
\(\Delta n=\frac{2v_s}{v}n\)
Listener passes stationary source
\(\Delta n=\frac{2v_o}{v}n\)
If \(v\gg v_o\)
\(\Delta n\approx\frac{2v_o}{v}n\)
▢ Wind Effect:

Table 1: Wind and Doppler Effect

Condition
Formula / Result
Wind in direction of sound
\(n'=\frac{v+v_w+v_o}{v+v_w-v_s}n\)
Wind opposite to sound
\(n'=\frac{v-v_w+v_o}{v-v_w-v_s}n\)
Wind at angle \(\theta\) with sound
\(v_w\cos\theta\) component used
Wind perpendicular to sound
No change in apparent frequency
▢ Reflection Doppler:

Table 1: Source / Observer Near Reflector

Case
Apparent Frequency
Car moving towards hill
\(n''=\frac{v+v_s}{v-v_s}n\)
Car moving away from hill
\(n''=\frac{v-v_s}{v+v_s}n\)
Astronaut / rocket signal reflected from reflector
Doppler shift occurs in two steps
Reflected light shift
\(\Delta n=\frac{2v}{c}n\)
Reflected wavelength shift
\(\Delta\lambda=\frac{2v}{c}\lambda\)
▢ Doppler Effect in Light:

Table 1: Light Doppler Effect

Point
Answer
Nature
Symmetrical
Depends on
Relative velocity only
Frequency shift
\(\Delta n=\frac{v}{c}n\)
Wavelength shift
\(\Delta\lambda=\frac{v}{c}\lambda\)
Star moving away
Red shift
Star approaching
Blue / violet shift
Red shift meaning
Apparent wavelength increases
Blue shift meaning
Apparent wavelength decreases and frequency increases
Expanding universe
Confirmed by red shift of distant galaxies
▢ Applications of Doppler Effect:

Table 1: Uses

Application
Purpose
RADAR
Locating distant objects using reflected radio/microwave waves
SONAR
Position of hidden submarines or icebergs
Stars and galaxies
Velocity measurement
Spectral lines
Determination of width
Sun
Speed of rotation
Tuning fork
Frequency determination
Twin / binary stars
Discovery and study
▢ Musical Sound and Noise:

Table 1: Sound Types

Term
Meaning
Musical sound
Quick succession of regular and periodic rarefactions and compressions without sudden amplitude change
Noise
Irregular and aperiodic rarefactions and compressions with sudden amplitude change
Tone
Musical sound of single frequency
Note
Musical sound containing two or more tones
Fundamental tone
Lowest frequency tone
Overtones
Tones other than fundamental tone
❖ Noise Level:
  • •
    Sound intensity more than 100 dB is called noise
  • •
    130 dB sound is painful and may cause hearing impairment
  • •
    Ticking watch is noise due to low frequency
  • •
    Pure sine wave in sound is called tone
▢ Characteristics of Musical Sound:

Table 1: Pitch, Loudness and Quality

Characteristic
Depends on
Meaning
Pitch
Frequency
Distinguishes shrill and grave sound
Loudness
Intensity + sensitivity of ear
Sensation of sound strength
Quality / Timbre
Waveform + overtones
Distinguishes same pitch and loudness from different instruments
❖ Pitch:
  • •
    Higher frequency → higher pitch
  • •
    Lower frequency → lower pitch
  • •
    Mosquito / buzzing bee has high pitch but low loudness
  • •
    Pitch of female voice is higher than male voice due to presence of more harmonics
  • •
    Pitch depends on frequency
❖ Loudness:
  • •
    Loudness depends on amplitude
  • •
    Greater amplitude → greater intensity → louder sound
  • •
    Loudness is subjective
❖ Quality:
  • •
    Depends on overtones
  • •
    Different overtones make same note sound different on different instruments
  • •
    Sweetness depends on periodicity and regularity
▢ Loudness and Intensity Level:
❖ **table:
    ❖ Important Relations:
      ◈ _*type: bullet
    1. If loudness changes by 1 dB, intensity changes by about 26%
    2. If \(n_1\) and \(n_2\) are intensity levels: \(n_1-n_2=10\log*{10}\frac{I_1}{I_2}\)
    3. Intensity of harmonic wave depends on both frequency and amplitude
    ▢ Sound Intensity Levels:

    Table 1: Common Sound Levels

    Source
    Intensity level
    Threshold of hearing
    0 dB
    Churches / hospitals
    10–20 dB
    Normal conversation
    50–60 dB
    Normal city traffic
    60–70 dB
    Alarm clock
    70–80 dB
    Damage threshold under prolonged exposure
    80–85 dB
    Jetliner 150 m overhead
    100–115 dB
    Running motorcycle
    115–120 dB
    Threshold of pain
    120–140 dB
    Jet plane taking off
    140–150 dB
    Launching space rocket
    160–180 dB
    ❖ Maximum Tolerable Sound: 120 dB
    ▢ Musical Intervals:

    Table 1: Intervals

    Term
    Relation
    Musical interval
    \(\frac{p}{q}\), where p and q are frequencies of two tones
    Octave
    2 : 1
    Fifth
    3 : 2
    Concord
    Pleasant combination of two tones
    Discord
    Unpleasant combination of two tones
    ▢ Musical Instruments:

    Table 1: Important Points

    Point
    Answer
    Air box
    Increases intensity / loudness
    Stringed instrument frequency increase
    Shorten and tighten string
    Walls of music hall
    Absorb sound; should not amplify, reflect or transmit too much
    Good audibility
    Reverberation time nearly 1 sec
    Temple / college bell
    Large size helps produce loud sound
    ▢ Infrasonic and Ultrasonic Notes:

    Table 1: Special Sound Facts

    Fact
    Answer
    Animals sense hurricane
    Due to infrasonic waves
    Infrasonic source
    Hurricane, earthquake, ocean wave, volcano
    Frequency range of infrasonic
    < 20 Hz
    Ultrasonic
    > 20,000 Hz
    SONAR
    Uses ultrasonic sound
    ▢ Read and Digest:

    Table 1: Important One-Liners

    Fact
    Answer
    Doppler effect in sound
    Not symmetrical
    Doppler effect in light
    Symmetrical
    Doppler effect frequency shift
    Independent of distance between source and observer
    Doppler effect not observed
    When relative velocity is zero
    Doppler effect not applicable
    Shock wave / supersonic wave
    Two photons approaching or receding
    Relative velocity = c
    Reflection of sound
    Causes reverberation
    Motion of source
    Changes apparent wavelength
    Motion of observer
    Changes apparent frequency
    Blue light from distant receding star
    Appears shifted towards red
    Ordinary conversation noise level
    About 65 dB
    Pitch
    Depends on frequency
    Loudness
    Depends on amplitude / intensity
    Quality
    Depends on overtones
    Sweetness
    Depends on periodicity and regularity
    Phon
    Unit of loudness
    Red shift
    Evidence of expanding universe
    ▢ High-Yield Recall:

    Table 1: Doppler and Musical Sound

    Fact
    Answer
    Doppler effect
    Apparent frequency change due to relative motion
    Approaching source-observer
    Frequency increases
    Receding source-observer
    Frequency decreases
    General sound formula
    \(n'=\frac{v\pm v_o}{v\mp v_s}n\)
    Light Doppler shift
    \(\Delta n=\frac{v}{c}n\)
    Wavelength shift
    \(\Delta\lambda=\frac{v}{c}\lambda\)
    Red shift
    Star/galaxy moving away
    Blue shift
    Star/galaxy approaching
    RADAR
    Radio Detection and Ranging
    SONAR
    Sound Navigation and Ranging
    Musical sound
    Regular periodic sound
    Noise
    Irregular aperiodic sound
    Tone
    Single frequency sound
    Note
    Two or more tones
    Fundamental tone
    Lowest frequency
    Overtones
    Remaining tones
    Pitch
    Frequency
    Loudness
    \(10\log*{10}(I/I_0)\)
    Threshold intensity
    \(10^{-12}Wm^{-2}\)
    Quality / timbre
    Overtones and waveform
    Octave
    2 : 1
    Fifth
    3 : 2
    Maximum tolerable level
    120 dB
    Q1.
    The driver of a car travelling with speed of 45 km/hr towards a person is also travelling by car towards source with same speed, the frequency of sound heard by person is provided that the driver's car produces frequency of 500 Hz:
    📅BP 2014
    Q2.
    Which can produce maximum pitch sound?
    📅BP 2013
    Q3.
    The loudness of sound is 40 dB. What is the intensity level of sound?
    📅BP 2013
    Q4.
    A window whose area is 2 m2 opens on a street where the street noise result in an intensity level at the window of 60 dB. How much 'acoustic power' enters the window via sound waves.
    📅BP 2009
    Q5.
    A source and listener is moving in the same direction with a velocity equal to half the velocity of sound what is the change in frequency.
    📅IOM 2013
    Q6.
    A car travels at a speed of 20 m/s towards a high wall. The driver sounds a horn of frequency 124 Hz. If velocity of sound in air is 330 m/s, the frequency of the reflected sound heard by the driver will be:
    📅MOE 2013
    Q7.
    A listener is moving away from stationary source of sound. The listener hears a sound of frequency:
    📅KU 2012
    Q8.
    A sound wave has intensity 10-3 W/m2. The intensity level in dB is equal to:
    📅KU 2012
    Q9.
    Which of the following sounds have maximum speed in air, sound produced by an explosion of a bomb, the roaring of a lion, buzzing sound of mosquito?
    📅BP 2013
    Q10.
    The notes that are separated by three octaves have a frequency ratio of:
    📅BP 2014
    Q11.
    A star is moving away from the earth. The wavelength of the light notes by the observer on the earth will be:
    📅BP 2015
    Q12.
    The intensity level due to waves of same frequency in a given medium are 1 bel and 5 bel. Then the ratio of their amplitudes is:
    📅MOE 2011
    Q13.
    A man is watching two trains, one leaving and the other coming towards him with equal speed of 4 m/s. If they sound their whistles, each of natural frequency of 240 Hz, the number of beats heard by (velocity of sound in air = 320 m/s) will be equal to:
    📅IOM 2014
    Q14.
    Speed of sound in air at a given temperature is 350 m/s. An engine which blows horn of 1200 Hz, is approaching the observer with velocity 50 m/s. The apparent frequency as heard by the observer will be:
    📅MOE 2013
    Q15.
    The apparent frequency noted by a moving listener away from the stationary source is 10% less than the real frequency. If the velocity of sound is 330 m/s, the velocity of the listener is:
    📅KU 2010
    Q16.
    A source of sound moves towards a stationary observer with a velocity equal to velocity of sound. If the source produces n waves/sec, the observer receives:
    📅BP 2012
    Q17.
    A tuning fork of frequency 90 Hz is sounded forward an observer moving with a velocity equal to 1/10th the velocity of sound. The note heard by the observer will have a frequency:
    📅MOE 2009
    Q18.
    A whistle is whirled in a circle of radius 1m and traverses the circular path twice per second. An observer is situated outside the circle but in its plane. If the velocity of sound is 332 m/s, then the interval between the highest and the lowest observed pitch is:
    📅IOM 2015
    Q19.
    A source of sound is moving with a velocity 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (velocity of sound is 350 m/s in air)
    📅BPKIHS 2011
    Q20.
    A whistle giving out sound of frequency 450 Hz approaches a stationary observer at a speed of 33 m/s. The frequency heard by the observer is:
    📅MOE 2010
    Q21.
    The musical interval between two notes of frequencies 320 Hz and 240 Hz is:
    📅BP 2013
    Q22.
    The apparent wavelength of the light from a star moving away from the earth is 0.4% more than its real wavelength. The velocity of the star is:
    📅IOM 2016
    Q23.
    The intensity level of two waves of same frequency in a given medium are 20 dB and 60 dB. Then the ratio of their amplitudes is:
    📅KU 2012
    Q24.
    A source of sound is moving away from a stationary observer with a speed equal to the speed of sound. The apparent frequency heard by the observer will be:
    📅KU 2010
    Q25.
    A whistle giving out 450Hz approaches a stationary observer at a speed of 33 m/s. The frequency heard by the observer in Hz is:
    📅MOE 2010
    Q26.
    A radar sends a signal of frequency 7.8 × 109/s towards an aeroplane moving with certain velocity. A frequency difference of 2.7 × 103/s is reflected from the aeroplane. Find the velocity of the aeroplane.
    📅IOM 2007
    Q27.
    When air space in a musical instrument is increased, what will increase?
    📅IOM 1997
    Q28.
    By which process, radio waves can be detected but not light waves in a closed room?
    📅MOE 2063/KU 08/09
    Q29.
    Quality of two sounds is different because:
    📅MOE 2062
    Q30.
    The intensity of sound gets reduced by 10% on passing through a block. If it passes through two such blocks, the intensity of the outgoing sound is:
    📅MOE 2009
    Q31.
    The loudness of two waves of same frequency in a given medium are 100dB & 20 dB respectively. How many times is the intensity of I1 is greater than I2?
    📅IE 2005
    Q32.
    A car is slowly moving towards a wall with velocity 2 m/s. If the frequency of horn blow by car is 700Hz, then no. of beats heard by the driver is (velocity of sound = 350 m/s):
    📅BPKIHS 2015
    Q33.
    A policeman sounds a whistle with frequency 300 Hz towards a car that moves towards him with a velocity of 5 m/s. Find the frequency of the whistle as heard by the driver of the car. (Velocity of sound in air = 320 m/s):
    📅ITE 2010
    Q34.
    A man in a car moving at 40 m/s is approaching a stationary siren emitting a sound frequency 510 Hz. The apparent frequency heard by the man is (take velocity of sound = 300 m/s):
    📅BPKIHS 2007
    Q35.
    A bus is moving towards a huge wall with a velocity of 5 m/s. The driver sounds a horn of frequency 200 Hz. The frequency of the beats heard by a passenger of the bus will be (speed of sound in air = 350 m/s):
    📅BPKIHS 1996
    Q36.
    The intensity of sound gets reduced by 10% on passing through a slab. The reduction in intensity on passing through two consecutive slabs would be:
    📅MOE 2008
    Q37.
    The driver of a car sounds a horn of frequency 600 Hz moving towards the hill with a speed 30 m/s. If speed of sound in air is 330 m/s, then frequency received by driver after reflection from hill is:
    📅BPKIHS 2014
    Q38.
    A man is watching two trains, one is leaving and the other is coming towards him with equal speed of 4 m/s. If they sound their whistles, each of natural frequency of 240 Hz, the number of beats heard by the man (velocity of sound in air = 320 m/s) will be:
    📅MOE 2012
    Q39.
    An object producing a pitch of 400 Hz approaches a stationary person in a straight line with a velocity of 200 m/s. Velocity of sound is 300 m/s. The person will note a change in frequency as the object flies past him equal to:
    📅IOM 2015
    Q40.
    A beam of sound is 106 times as intense as that with minimum audible intensity. The loudness of the beam is thus:
    📅BP 2011
    Q41.
    An engine is moving on a circular track of radius 100 m with the speed of 20 m/s. What will be the frequency observed by an observer standing stationary at the centre of the circular path when the engine blows a whistle of frequency 500 Hz?
    📅IOM 2016
    Q42.
    When both source and observer approach each other with a velocity equal to half of the velocity of sound, the change in frequency of sound as detected by the listener is:
    📅MOE 2014
    Q43.
    A source of sound produces waves of λ = 40 cm in air. It is moving with a velocity one-fourth the velocity of sound towards east. The apparent wavelength noted by a man in opposite direction is:
    📅BP 2010
    Q44.
    At what speed should a source of sound move so that observer finds the apparent frequency equal to half of the original frequency:
    📅KU 2011
    Q45.
    A galaxy is approaching the earth with a velocity of 105 m/s. As observed on the earth, the shift in the spectral line of wavelength 5700 Å will be:
    📅IOM 2017
    Q46.
    Two whistles A and B produce notes of frequencies 600 Hz and 596 Hz respectively. There is a listener at the middle of the line joining them. Now the whistle B and the listener start moving with the speed 30 m/s away from the whistle A. If the speed of the sound is 330 m/s, how many beats will be heard by the listener?
    📅BP 2016
    Q47.
    A whistle of frequency 500 Hz is tied to a end of a string of length 1.2 m revolves at 400 rev/min. A listener standing some distance away in the plane of rotation of whistle hears frequencies in the range: (speed of sound = 340 m/s):
    📅MOE 2015
    Q48.
    In the spectrum of light of a luminous heavenly body, the wavelength of spectral line is measured to be 4747 Å while actual wavelength of the spectral line is 4700 Å. Then relative velocity of heavenly body w.r.t earth is:
    📅IOM 2018
    Q49.
    The wavelength of light observed on the earth, from a moving star is found to decrease by 0.05% relative to the earth, the star is:
    📅BPKIHS 2017
    Q50.
    An astronaut in a rocket approaching towards the moon sends a radio wave of frequency 5 × 109 Hz towards the moon. The frequency received by him is 9 × 106 Hz more than the actual frequency. Then relative velocity of rocket w.r.t moon is:
    📅IOM 2019
    Q51.
    Two cars are moving on two perpendicular roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. If the first car blows a horn of frequency 280 Hz, then the frequency of the horn heard by the driver of the second car when line joining the car makes an angle of 45° with roads will be:
    📅MOE 2016
    Q52.
    A source of sound emits 200 μW power which is uniformly distributed over a sphere of radius 10 m. What is the loudness of sound on the surface of the sphere? (log102 = 0.3):
    📅BP 2017
    Q53.
    A person is standing on a railway station. When a train is approaching him, the frequency of whistle heard by him is 220 Hz, but when the train has crossed him, the frequency heard by him is 184 Hz. The actual frequency of the whistle is:
    📅BPKIHS 2015
    Q54.
    A person is driving in a car with velocity 30 m/s towards the rock. The person honked the car with frequency 600 Hz & the sound is reflected from rock. The apparent frequency heard by the person is? [velocity of sound 330 m/s]:
    📅IOM 2016
    Q55.
    Stationary observer heard twice the original frequency of the source moving towards the observer. What is the velocity of source? [Given the velocity of sound 332 m/s]:
    📅IOM 2016
    Q56.
    A sound having intensity of 10-4 W/m2 has loudness of:
    📅KU 2017
    Q57.
    When both source and observer moving in the same direction with the velocity half that of sound. Then the percentage of increase in frequency will be:
    📅IOM 2017