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1 Last Name irst Name Date 16.1 The Nature of Waes 16.2 Periodic Waes 16.3 The Speed of a Wae in a String Conceptual Questions 1,2,3,7, 8, 11 page 503 Problems 2, 4, 6, 12, 15, 16 page Types of Waes There are two main types of disturbances in waes. The wae created by Hand A is a Wae. The wae created by Hand B is a Wae. There is a third type? Can you guess what is? There also two other classifications of waes: Examples: Waes in a Spring, Sound, Water or Ocean Waes, Example: Radio Waes, Microwaes, Infrared Waes, Visible, Ultraiolet, X Rays, Gamma Rayse The Relationship between Waelength, requency and Velocity Which train has the greatest waelength (λ )? A or B Assuming the speed of the trains are the same, which train will hae more trains pass a stationary point in a gien time? A or B Time for one wae to pass is called a Period (T) How often cars pass is called requency (f) As waelength increases Period will (increase or decrease) Wae Equations: f = 1 T Train speed = waes per period or = λ T What are units of T?? f?

2 Speed of a Wae The material which a wae is moing through is called the MEDIUM. (What is plural of medium?) Example: Sound traels faster in higher density substances. Speed of sound in air (which aries with Temperature and Humidity) is about 340 m/s. The motion of a wae in a string (such as a guitar string) is well understood and accurately quantified with the following Equation: = m/l where is the Tension in the String (N), m is the Mass (kg) and L the unit Length (m). Notice that m/l is a Linear Density for the string. As the orce increases the speed (increases / decreases). As the Linear Density increases the speed (increases / decreases). AT AN INTERACE OR BOUNDARY An interface (or boundary) is when a wae moes from one medium to another. Here are two examples: Moing from low to high density string and moing from high to low density string. What happens to the speed of the wae as it moes from low density to high density? (Increases or Decreases) What happens to the speed of the wae as it moes from low density to high density? (Increases or Decreases) The requency of the wae stays the same when passing from one medium to another. What happens to the waelength when a wae moes from low density to high density? (Increases or Decreases) What happens to the waelength when a wae moes from high density to low density? (Increases or Decreases)

3 Conceptual Questions 1,2,3,7, 8, 11 page Considering that nature of a water wae, describe the motion of a fishing float on the surface of a lake when a wae passes beneath the float. Is it really correct to say that the float bobs straight up and down? Explain. As igure 16.4 shows, in a water wae, the wae motion of the water includes both transerse and longitudinal components. The water at the surface moes on nearly circular paths. When the wae passes beneath a fishing float, the float will simultaneously bob up and down, as well as moe back and forth horizontally. Thus, the float will moe in a nearly circular path in the ertical plane. It is not really correct, therefore, to say that the float bobs straight "up and down." 2. Domino Toppling is one entry in the Guinness Book of World Records. The eent consists of lining up an incredible number of dominoes and then letting them topple, one after another. Is the disturbance that propagates along the line of the dominoes transerse, longitudinal, or partly both? Explain. REASONING AND SOLUTION "Domino Toppling" is an eent that consists of lining up an incredible number of dominoes and then letting them topple, one after another. As the dominoes topple, their displacements contain both ertical and horizontal components. Therefore, the disturbance that propagates along the line of dominoes has both longitudinal (horizontal) and transerse (ertical) components. 3. Suppose that a longitudinal wae moes along a Slinky at a speed of 5 m/s. Does one coil of the Slinky moe through a distance of 5 m in one second? Justify your answer. REASONING AND SOLUTION A longitudinal wae moes along a Slinky at a speed of 5 m/s. We cannot conclude that one coil of the Slinky moes through a distance of 5 m in one second. The quantity 5 m/s is the longitudinal wae speed, speed ; it specifies how fast the disturbance traels along the spring. The wae speed depends on the properties of the spring. Like the transerse wae speed, the longitudinal wae speed depends upon the tension in the spring and its linear mass density m/l. As long as the tension and the linear mass density remain the same, the disturbance will trael along the spring at constant speed. The particles in the Slinky oscillate longitudinally in simple harmonic motion with the same amplitude and frequency as the source. As with all particles in simple harmonic motion, the particle speed is not constant. The particle speed is a maximum as the particle passes through its equilibrium position and reaches zero when the particle has reached its maximum displacement from the equilibrium position. The particle speed depends upon the amplitude and frequency of the particle's motion. Thus, the particle speed, and therefore the longitudinal speed of a single coil, depends upon the properties of the source that causes the disturbance.

4 7. One end of each of two identical strings is attached to a wall. Each string is being pulled tight by someone at the other end. A transerse pulse is sent traeling along one of the strings. A bit later an identical pulse is sent traeling along the other string. What, if anything, can be done to make the second pulse catch up with and pass the first pulse? Account for your answer. (A pulse is a single piece of a wae. What you do in a football stadium is actually a pulse rather than a wae) REASONING AND SOLUTION One end of each of two identical strings is attached to a wall. Each string is being pulled tightly by someone at the other end. A transerse pulse is sent traeling along one of the strings. A bit later, an identical pulse is sent traeling along the other string. In order for the second pulse to catch up with the first pulse, the speed of the pulse in the second string must be increased. The speed of the transerse pulse on the second string is gien by Equation 16.2: wae /( m / L). This equation indicates that we can increase the speed of the second pulse by increasing the tension in the string. Thus, the second string must be pulled more tightly. 8. Would it take any time for a transerse wae to trael the length of the mass less rope? Justify your answer. REASONING AND SOLUTION In Section 4.10 the concept of a "massless" rope is discussed. or a truly massless rope, the linear density of the rope, m/l, is zero. rom Equation 16.2, wae /( m / L), the wae speed would be infinite if m/l were zero. Therefore, if the rope were really massless, the speed of transerse waes on the rope would be infinite, and a transerse wae would be instantaneously transmitted from one end of the rope to the other. It would not take any time for a transerse wae to trael the length of a massless rope. 11. A loudspeaker produces a sound wae. Does the waelength of the sound increase, decrease, or remain the same, when the wae traels from air into water? Justify your answer. A loudspeaker produces a sound wae. The sound wae traels from air into water. As indicated in Table 16.1, the speed of sound in water is approximately four times greater than it is in air. We are told in the hint that the frequency of the sound wae does not change as the sound enters the water. The relationship between the frequency f, the waelength, and the speed of a wae is gien by Equation 16.1: f. Since the wae speed increases and the frequency remains the same as the sound enters the water, the waelength of the sound must increase.

5 Problems 2,4,6,12,15,16 page A woman is standing in the ocean, and she notices that after a wae crest passes, fie more crests pass in a time of 50.0 s. The distance between two successie crests is 32 m. Determine the, if possible, the wae s (a) period, (b) frequency, (c) waelength, (d) speed, and (e) amplitude. If it is not possible to determine any of these quantities, then so state. a. The period is the time required for one complete cycle of the wae to pass. The period is also the time for two successie crests to pass the person. b. The frequency is the reciprocal of the period, according to Equation c. The waelength is the horizontal length of one cycle of the wae, or the horizontal distance between two successie crests. d. The speed of the wae is equal to its frequency times its waelength (see Equation 16.1). e. The amplitude A of a wae is the maximum excursion of a water particle from the particle s undisturbed position. SOLUTION a. After the initial crest passes, 5 additional crests pass in a time of 50.0 s. The period T of the wae is 50.0 s T s b. Since the frequency f and period T are related by f = 1/T (Equation 10.5), we hae 1 1 f Hz T 10.0 s

6 4. One tsunami, generated off the Aleutian islands in Alaska, had a waelength of 750 km and traeled a distance of 3700 km in 5.3 hours. (a) What was the speed (in m/s) of the wae? or reference, the speed of the wae a 747 jetliner is about 250 m/s. ind the wae s (b) frequency and (c) period. The speed of a Tsunamis is equal to the distance x it traels diided by the time t it takes for the wae to trael that distance. The frequency f of the wae is equal to its speed diided by the waelength, f = / (Equation 16.1). The period T of the wae is related to its frequency by Equation 10.5, T = 1/f. SOLUTION a. The speed of the wae is (in m/s) x m 1 h t 5.3 h 3600 s m/s b. The frequency of the wae is f 190 m/s Hz m (16.1) c. The period of any wae is the reciprocal of its frequency: T s f Hz (10.5)

7 6. A person lying on an air mattress in the ocean rises and falls through one complete cycle eery fie seconds. The crests of the wae causing motion are 20.0 m apart. Determine (a) the frequency and (b) the speed of the wae. The period of the wae is the same as the period of the person, so T = 5.00 s. a. f = 1/T = Hz (10.5) b. = f = (20.0 m)(0.200 Hz) = 4.00 m/s (16.1) 12. A wire is stretched between two posts. Another wire is stretched between two posts that are twice as far apart. The tension in the wires is the same, and they hae the same mass. A transerse traels on the wire with a speed of 240 m/s. What would be the speed of the wae on the wire? The speed of a transerse wae on a wire is gien by / m/ L (Equation 16.2), where is the tension and m/l is the mass per unit length (or linear density) of the wire. We are gien that and m are the same for the two wires, and that one is twice as long as the other. This information, along with knowledge of the wae speed on the wire, will allow us to determine the speed of the wae on the wire. SOLUTION The speeds on the and wires are: [Longer wire] ml / [Shorter wire] ml / Diiding the expression for by that for gies ml / ml / L L Noting that = 240 m/s and that L = 2L, the speed of the wae on the wire is L 2L 240 m/s 240 m/s m/s L L

8 15. Two wires are parallel, and one is directly aboe the other. Each has a length of 50.0 m and a mass per unit length of kg/m. Howeer, the same tension in a wire A is N, and the tension in wire B is N. Transerse waes pulses are generated simultaneously, one at the left end of the wire A and one at the right end of wire B. The pulses trael towards each other. How much time does it take until the pulses pass each other? Each pulse traels a distance that is gien by t, where is the wae speed and t is the trael time up to the point when they pass each other. The sum of the distances traeled by each pulse must equal the 50.0-m length of the wire, since each pulse starts out from opposite ends of the wires. SOLUTION Using A and B to denote the speeds on either wire, we hae Soling for the time t and using Equation 16.2 A t + B t = 50.0 m m/ L, we find t 50.0 m A B 50.0 m A m / L B m / L 50.0 m N kg/m N kg/m 0.17 s

9 16. The drawing shows two transerse waes traeling on two strings. The linear density of each string is kg/m, and the tension is proided by a 26-N block that is hanging from the string. Determine the speed of the wae in part (a) and part (b) of the drawing. The speed of a transerse wae on a string is gien by / m/ L (Equation 16.2), where is the tension and m/l is the mass per unit length (or linear density) of the string. The strings are identical, so they hae the same mass per unit length. Howeer, the tensions are different. In part (a) of the text drawing, the string supports the entire weight of the 26-N block, so the tension in the string is 26 N. In part (b), the block is supported by the part of the string on the left side of the middle pulley and the part of the string on the right side. Each part supports one-half of the block s weight, or 13 N. Thus, the tension in the string is 13 N. SOLUTION a. The speed of the transerse wae in part (a) of the text drawing is 26 N m/s ml / kg/m b. The speed of the transerse wae in part (b) of the drawing is 13 N m/s ml / kg/m