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Name: Neil Kyle O. Maniquis Section: 10 - Copernicus Date Submitted: November 18, 2021 WORKSHEET NO. 1 DOPPLER EFFECT KEY IDEAS Terms DOPPLER EFFECT Description The apparent change in the frequency of a wave whenever there is relative motion between a source of waves and an observer. ๏ There is relative motion between two objects when the distance between them is changing (either increasing or decreasing) in time ๏ The observed frequency will be higher than the actual frequency when the distance between the source and observer is decreasing (approaching) ๏ The observed frequency will be lower than the actual frequency when the distance between the source and the observer is increasing in time (receding) ๏ can be observed in all waves: mechanical or electromagnetic Observed Frequency ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐๐๐ ๐๐๐ฃ๐๐ ๐๐ = ๐๐ ( ) ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐กโ๐ ๐ ๐๐ข๐๐๐ Note on relative velocity Consider two objects, A and B, that are traveling in the same direction along a straight path. vB vA The velocity of car A relative to car B is defined as: ๐ฃ๐ด๐ต = ๐ฃ๐ด โ ๐ฃ๐ต If car B is traveling in the opposite direction, then ๐ฃ๐ด๐ต = ๐ฃ๐ด โ (โ๐ฃ๐ต ) = ๐ฃ๐ด + ๐ฃ๐ต Bow wave Occurs when the source of the wave is traveling at a speed equal to the speed of the wave if produces. ๏ Also known as wave barrier SHOCK WAVE A shock wave is produced when an object travels at a speed greater than the speed of the wave ๏ the object need not be a source of waves ๏ it is formed by superposition of wavefronts behind the object ๏ for sound waves, the sound produced is called the sonic boom MACH NO. The slope of the shock wave depends on the ratio of the speed of the wave to the speed of the object. sin ๐ = ๐ฃ๐ค 1 = ๐ฃ๐ ๐ The Mach no. of a moving object is defined as the ratio of the speed of the object to the speed of sound ๐= ๐ฃ๐๐๐๐๐๐ก ๐ฃ๐ ๐๐ข๐๐ ๏ Objects with M > 1 are traveling at supersonic speed. They generate shock waves ๏ Objects with M < 1 are traveling at subsonic speed. Doppler effect can be observed in this case. SAMPLE PROBLEMS 1. A railroad train is traveling at 25 m/s in still air. The frequency of the note emitted by the locomotive whistle is 400 Hz. What is the frequency of the sound heard by a stationary listener (a) in front of the locomotive? (b) behind the locomotive? Solution: Draw a diagram showing the relative position of the source and the observer. Indicate the velocities of the source, observer and the wave. a. for the observer in front of the train (Observer A) ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐๐๐ ๐๐๐ฃ๐๐ ๐๐ด = ๐๐ ( ) ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐กโ๐ ๐ ๐๐ข๐๐๐ ๐ 340 ๐ โ 0 ๐ฃ๐ค โ ๐ฃ๐ด ๐๐ด = ๐๐ ( ) = 400 ๐ป๐ง ( ๐ ๐) = 432 ๐ป๐ง ๐ฃ๐ค โ ๐ฃ๐ 340 ๐ โ 25 ๐ Note: the wave and the source are traveling in the same direction. b. for the observer behind the train (observer B) ๐ 340 โ 0 ๐ฃ๐ค โ ๐ฃ๐ต ๐ ๐๐ต = ๐๐ ( ) = 400 ๐ป๐ง ( ๐ ๐) = 373 ๐ป๐ง ๐ฃ๐ค โ ๐ฃ๐ 340 + 25 ๐ ๐ Note: in this case, the wave and the source are traveling in opposite directions. 2. A stationary motion detector sends sound waves of frequency 0.150 MHz toward a truck approaching at a speed of 45 m/s. What is the frequency of the wave reflected back to the detector? Solution: To solve this problem, we break the situation into two parts: First Part: the motion detector (source) sends waves toward the truck (observer). The frequency of sound received by the truck is given by ๐ฃ๐ค + ๐ฃ๐ ๐๐ = ๐๐ ( ) ๐ฃ๐ค Second part: The truck (source) reflects the waves back to the motion detector. The frequency reflected back to the detector is thus ๐ฃ๐ค ๐ฃ๐ค + ๐ฃ๐ ๐ฃ๐ค ๐ฃ๐ค + ๐ฃ๐ 340 + 45 ๐ โฒ = ๐๐ ( )= ( )( )= ( ) = 0.150๐๐ป๐ง ( ) = 0.2 ๐๐ป๐ง ๐ฃ๐ค โ ๐ฃ๐ ๐ฃ๐ค ๐ฃ๐ค โ ๐ฃ๐ ๐ฃ๐ค โ ๐ฃ๐ 340 โ 45 EXERCISES 1. Five expanding wave fronts from a moving sound source are shown. The dots represent the centers of the respective circular wave fronts, which is the location of the source when that wave front was emitted. The frequency of the sound emitted by the source is constant. a. Indicate on the figure the direction of motion of the source. Which sound wave front was produced first (label it)? How do you know? Explain. The labeled sound wave front is the first produced and this is known because it has the largest diameter meaning it has been the first sound wave front produced. The explanation sounds rather subjective but another reasoning for this is that, we know that given a point (source), if an observer โs observance of the sounds is more frequent, then the sound wave is heading towards the observer, which is observer B and since it is heading towards observer B, the point nearest to observer B is the source of the newest circular wave front formed and the farthest from it, is the source of the oldest circular wave. b. Do the observers at locations A and B hear the same frequency of sound? If not, which one hears a higher frequency? Explain. No. Observer B hears a higher frequency because the speed of the wave is constant and it can be seen that the wavefronts towards B are more compressed and since they move in the same speed, more wavefronts will arrive at B before at A. c. Assume that the sound wave you identified in part a as the first wavefront produced marks the beginning of the sound. Do the observers at A and B first hear the sound at the same time? If not, which one hears the sound first? Explain. Based on the figure, the first point is equidistant to both observers A and B, and since it has been stated that the objective frequency is the same, yes, they will hear the first sound at the same time. 2. You are standing at x = 0 m, listening to a sound that is emitted at a frequency fo. At t = 0s, the sound source is at x = 20 m and moving toward you at a STEADY 10 m/s. Draw a graph showing the frequency you hear from t = 0s to t = 4s. ONLY the shape of the graph is important, not the numerical value of f. 3. Two train whistles, A and B, each have a frequency of 392 Hz. A is stationary and B is moving toward the right (away from A) at a speed of 35 m/s. A listener is between the two whistles and is moving toward the right with a speed of 15 m/s. a. What is the frequency from A as heard by the listener? //assuming still air ๐ ๐ 340 ๐ โ 15 ๐ ) 392 ๐ป๐ง( ) = 374.71 ๐ป๐ง ๐ 340 ๐ b. What is the frequency from B as heard by the listener? ๐ ๐ 340 ๐ + 15 ๐ 392 ๐ป๐ง( ๐ ๐) = 371.09 ๐ป๐ง 340 ๐ + 35 ๐ 4. A bat flies toward a wall at a speed of 10 m/s, emitting a steady sound of frequency 2000 Hz. At what frequency does the bat hear the reflected sound?(Hint: Break this problem into two parts, first with the bat as the source and the wall as the listener and then with the wall as the source and the bat as the listener) Let fโ be the observed frequency of the sound and fโโ be the observed frequency of the reflected sound. ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐๐๐ ๐๐๐ฃ๐๐ ) ; ๐๐๐ ๐๐๐ฃ๐๐ = ๐ค๐๐๐; ๐ ๐๐ข๐๐๐ = ๐๐๐ก ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐กโ๐ ๐ ๐๐ข๐๐๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐๐๐ ๐๐๐ฃ๐๐ ๐ โฒโฒ = ๐โฒ ( ) ; ๐๐๐ ๐๐๐ฃ๐๐ = ๐๐๐ก; ๐ ๐๐ข๐๐๐ = ๐ค๐๐๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ ๐๐ ๐กโ๐ ๐ค๐๐ฃ๐ ๐๐๐๐๐ก๐๐ฃ๐ ๐ก๐ ๐กโ๐ ๐ ๐๐ข๐๐๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ + ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ โฒ = ๐๐ ( ) ; ๐ โฒโฒ = ๐โฒ ( ) ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ โ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ + ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ โฒโฒ = ๐๐ ( )( ) ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ โ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ + ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ โฒโฒ = ๐๐ ( )( ) ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ โ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ + ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ โฒโฒ = ๐๐ ( ) ๐ฃ๐๐๐๐๐๐ก๐ฆ๐ค๐๐ฃ๐ โ ๐ฃ๐๐๐๐๐๐ก๐ฆ๐๐๐ก ๐ ๐ ๐ 340 ๐ + 10 ๐ 350 ๐ โฒโฒ ๐ = (2000 ๐ป๐ง) ( ๐ ๐ ) = 2000 ๐ป๐ง โ ๐ = 2121.21 ๐ป๐ง 340 ๐ โ 10 ๐ 330 ๐ ๐ โฒ = ๐๐ (