The Doppler effect. Explanation. The Doppler-shifted frequency:

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Shanon Hines
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approaching and an apparent downward shift in frequency when the observer and the source is receding.

1 (I) The Doppler effect The Doppler Effect is a phenomenon observed whenever the source of waves is moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer and the source are approaching and an apparent downward shift in frequency when the observer and the source is receding. The Doppler Effect can be observed to occur with all types of waves - most notably water waves, sound waves, and light waves. Explanation The Doppler-shifted frequency: f L f s 1 vs 1 v v s = velocity of the source, v =velocity of wave (sound) in air Sign: - approaching source => f L >f s + approaching source => f L <f s

P2/ In patrolling mode, a bat, emits a sound with a frequency of 40 khz. When attacking an insect the bat changes the frequency of the emitted sound to 85 khz.

2 P1. A police car s siren emits a sinusoidal wave with frequency ƒ S = 300 Hz. The speed of sound is 340 m/s and the air is still. (a) Find the wavelength of the waves if the siren is at rest. (b) Find the wavelengths of the waves in front of and behind the siren if it is moving at 30m/s. P2/ In patrolling mode, a bat, emits a sound with a frequency of 40 khz. When attacking an insect the bat changes the frequency of the emitted sound to 85 khz. a) Does a human being hear these sounds? b) What are the wavelengths of the emitted sounds? c) Why in attacking mode the bat is increasing the frequency of the emitted sound? (Take the speed of sound in air to be v = 340 m/s.)

3 Answer: (a) No, the audible frequency range is between 20Hz-20 KHz. 3 (b) The wavelength is: v / f 340 / 40*10 0, 0085m 8.5mm (c) Having in view that the precision in echolocation at 40KHz is limited by (8.5mm), in order to catch an insect the precision can be increades by increasing frequency and consequently decreasing. 3 v / f 340 /(85*10) 0, 004 m 4 mm P3/ One way to tell if a mosquito is about to sting is to listen for the Doppler shift as the mosquito is flying. The buzzing sound of a mosquito s wings is emitted at a frequency of 1050 Hz. a) If you hear a frequency of 1034 Hz, does this mean that the mosquito is coming in for a landing or that it has just bitten you and is flying away? b) At what velocity is the mosquito flying? Use the following equation: 1 fl f (Doppler effect, moving source and fixed s Vs 1 V listener), where: v is the sound velocity in air, v is the sound velocity in air (340 m/s), v S is the source velocity, f s is the frequency of the sound emitted by the source and f L the frequency heard by the listener. Answer: (a) 1034Hs<1050Hz. It means that the Dopplr shifted frequency is smaller than the rest frequency, so that the source is mowing away. Unfirtunatelly, the mosquito just biten and flying away 1 (b) Using the equation fl f with the + sign corresponding to moving away s Vs 1 V source, one finds that v s =v(f L /f s -1)=5.2m/s.

P4: The Doppler effect for the electromagnetic waves emitted by galaxies is a proof of the Universe expansion In astronomy, the Doppler effect was originally studied in the visible part of the

4 P4: The Doppler effect for the electromagnetic waves emitted by galaxies is a proof of the Universe expansion In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all portions of the spectrum. Also, because of the inverse relationship between frequency and wavelength, we can describe the Doppler shift in terms of wavelength. Radiation is redshifted when its wavelength increases, and is blueshifted when its wavelength decreases. Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects move toward or away from Earth. For example the spectral lines emitted by hydrogen gas in distant galaxies is often observed to be considerably redshifted. The spectral line emission, normally found at a wavelength of 21 centimeters on Earth, might be observed at 21.1 centimeters instead. Answer: using the equations c u f f0 f0 in case of approaching source (blue shift) and c u f f0 f0 in case c u c u of moving away source (red shift), the 0.1 centimeter redshift would indicate that the gas is moving away from Earth at over 1,400 kilometers per second (over 880 miles per second).

Shock waves As the speed of the airplane Vs approaches the speed of sound V the wavelength approaches zero and the wave crests pile up on each other.

5 Shock waves As the speed of the airplane Vs approaches the speed of sound V the wavelength approaches zero and the wave crests pile up on each other. The airplane must exert a large force to compress the air in front of it; by Newton s third law, the air exerts an equally large force back on the airplane. Hence there is a large increase in aerodynamic drag (air resistance) as the airplane approaches the speed of sound, a phenomenon known as the sound barrier. When is greater in magnitude than the source of sound is supersonic, and Eqs. for the Doppler effect no longer describe the sound wave in front of the source. The inserse of sin is called the Mach number M=1/ sin.

P1. A jet airplane is flying at a constant altitude at a steady speed greater than the speed of sound. Describe what observers at points A, B, and C hear at the instant shown in Fig.

6 P1. A jet airplane is flying at a constant altitude at a steady speed greater than the speed of sound. Describe what observers at points A, B, and C hear at the instant shown in Fig. BELOW, when the shock wave has just reached point B. Explain your reasoning. Answer In front of the cone (A) a listener hears no sound, when the shock wave arrives the listener (B) hears a boom (sudden increase of pressure) and after (C) (inside the cone), a Doppler shifted sound for moving away source. P2. An airplane is flying at Mach 1.75 at an altitude of 8000 m, where the speed of sound is 320m/s. How long after the plane passes directly overhead will you hear the sonic boom?

7 Test Your Understanding What would you hear if you were directly behind (to the left of ) the supersonic airplane in Fig ? (i) a sonic boom; (ii) the sound of the airplane, Dopplershifted to higher frequencies; (iii) the sound of the airplane, Doppler-shifted to lower frequencies; (iv) nothing.

The Doppler Effect is the change in frequency observed when a source of sound waves is moving relative to an observer.

Doppler Effect The Doppler Effect is the change in frequency observed when a source of sound waves is moving relative to an observer. Examples of the Doppler effect are: Hearing an increase in a car horn