Note on Doppler Effect, Waves and Noise Pollution

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Effect of Medium

If the medium travels to the direction of sound wave then frequency of sound increases and if medium travels in opposite direction of sound wave then frequency of sound decreases. Apparent change in frequency, if direction of medium and sound wave is same, given by

\begin{align*} F’ &=\left [ \frac {(v + v_m) – u_0}{(v + v_m) –u_s} \right ] \times f \\ \end{align*}

Apparent change in frequency, if direction of medium and sound wave is opposite to each other. Then,

\begin{align*} F’ &=\left [ \frac {(v - v_m) – u_0}{(v - v_m) –u_s} \right ] \times f \\ \text {where,} \: v_m &= \text { velocity of medium} \\ v &= \text {velocity of sound} \\ u_o &= \text {velocity of observer} \\ u_s &= \text {velocity of source} \\ f’ &= \text {change in frequency} \\ \end{align*}

Limitation of Doppler Effect
  • The Doppler’s principle can only be applied in the cases where the relative velocity between the source and observer is less than the velocity of sound.
  • This principle is not applicable if the source moves towards the observer with supersonic velocity.

Doppler’s Principle in Light

When a star recedes from the earth, its spectral lines are displaced towards the red end which indicates an increase in wavelength and is called a red shift. When a star approaches the earth, the spectral lines are displaced towards the violet and there is a decrease in wavelength, the velocity known as blue shifts. If λ is the wavelength of light emitted by the tar in the stationary position, λ’ be the wavelength when it is in motion, us is the velocity of approach of the star and c is the velocity of light, then

\begin{align*} \lambda ‘ &= \left ( \frac {c – u_s}{c} \right ) \lambda = \left ( 1 - \frac {u _s}{c} \right ) \lambda = \lambda - \frac {u_s}{c} \lambda \\ \text {or,} \: \frac {u_s}{c} \lambda &= \lambda - \lambda ‘ \\ \text {or,} \: u_s &= \frac {c(\lambda - \lambda ‘)}{\lambda } \\ \end{align*}

When λ and the shift (λ – λ’) are known, the velocity of star can be calculated. The measurement of red shift of light from galaxies suggests that the universe is expanding.

Application of Doppler Effect
  1. Velocity of approaching or receding stars can be determined by using Doppler’s principle using the formula,
    $$ u_s = \frac {c(\lambda - \lambda ‘ )} {\lambda } $$
  2. Red Shift: it has been observed that some distant nebulae are moving away with a velocity greater than 20 × 103 km/s and the spectral lines appear to shift towards the red end of the spectrum by 200 Ao. This gives the idea that universe is expanding.
  3. In radar: microwaves emitted from a radar transmitter are sent out towards the target and after reflection from the target, these waves are picked up by the receiving the station of radar. If the aeroplane is approaching the observing station, there will be an increase in frequency or decrease in frequency or decrease in the wavelength of microwaves. But is the aeroplane is moving away from the observing station, there will be a decrease in frequency or increase in wavelength.
  4. In SONAR (Sound Navigation and Ranging): Doppler’s principle is used in SONAR for the detection of submarine or group of fishes under water in the sea. The SONAR makes use of ultrasounds of frequencies more than 20 kHz and the reflected signals can be used for calculating the speed approaching or receding of submarines under water.
Range of Hearing

Normal human ears can hear only those waves whose frequency lies between 20 Hz and 20,000 Hz. The sound waves having a frequency between 20 Hz and 20, 000 Hz are known as sound waves which are an audible range of frequency. The waves having a frequency less than 20 Hz and greater than 20, 000 Hz cannot be heard by human ear.

Infrasonic and Ultrasonic Waves

Infrasonic Wave

The waves of frequency less than 20 Hz are known as infrasonic waves. These waves are not audible to a human ear. For example vibration of earth’s surface and a sound of animals like elephants, rhinoceros and whales etc.

Ultrasonic Wave

The waves of frequency greater than 20, 000 Hz are known as ultrasonic waves or ultrasound. It is not audible for the human ear. Example: sound produced by jet planes, bomb blasting etc. In the case of bat, wings of bat produce ultrasound which is transmitted towards the prey. It receives quickly and which position is the prey, so, the bat can easily catch the prey.

Uses of Ultrasound

  1. For welding plastics
  2. To diagnosis of human disease of human disease (Eg: cancer in stomach)
  3. To check the development of unborn baby
  4. To kill bacteria in the liquid
  5. To find faults and cracks in metals
  6. To determine the depth of a sea

Noise Pollution

The sound of loudness greater than 45 Db is harmful to human ear which produce noise pollution. According to WHO, the loudness of city must be balanced up to 45 Db.

Effects of Noise Pollution
  1. It causes permanent deafness.
  2. It causes a loss in heavy power.
  3. It causes a headache, blood pressure etc.
  4. It resists doing work properly.
  5. It causes disease like neurosis, insomnia, and hypertension, behavioral and emotional stress.
  6. It interferes with a speech of people.
Control of Noise Pollution
  1. Generating awareness about the cause of pollution.
  2. Designing and fabricating silencing devices in aircraft engines or any other machines.
  3. Room walls should be covered with sound absorbers.
  4. Workers exposed to noise should be given bear plugs.
  5. It can be controlled by banning the air horn.
  6. It can be controlled by running loudspeaker, radio and another music system at low volumes.

References

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

If the medium travels to the direction of a sound wave then a frequency of sound increases and if medium travels in opposite direction of a sound wave then the frequency of sound decreases.

When a star recedes from the earth, its spectral lines are displaced towards the red end which indicates an increase in wavelength and is called a red shift.

When a star approaches the earth, the spectral lines are displaced towards the violet and there is a decrease in wavelength, the velocity known as blue shifts.

 The sound waves having a frequency between 20 Hz and 20, 000 Hz are known as sound waves which are an audible range of frequency. 

The waves of frequency less than 20 Hz are known as infrasonic waves. 

The sound of loudness greater than 45 Db is harmful to human ear which produce noise pollution.

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