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Unformatted text preview: 1451 Chapter 15 Traveling Waves Conceptual Problems 1 [SSM] A rope hangs vertically from the ceiling. A pulse is sent up the rope. Does the pulse travel faster, slower, or at a constant speed as it moves toward the ceiling? Explain your answer. Determine the Concept The speed of a transverse wave on a uniform rope increases with increasing tension. The waves on the rope move faster as they move toward the ceiling because the tension increases due to the weight of the rope below the pulse. 2 A pulse on a horizontal taut string travels to the right. If the ropes mass per unit length decreases to the right, what happens to the speed of the pulse as it travels to the right? ( a ) It slows down. ( b ) It speeds up. ( c ) Its speed is constant. ( d ) You cannot tell from the information given. Determine the Concept The speed v of a pulse on the string varies with the tension F T in the string and its mass per unit length according to T F v = . Because the ropes mass per unit length decreases to the right, the speed of the pulse increases. ( ) b is correct. 3 As a sinusoidal wave travels past a point on a taut string, the arrival time between successive crests is measured to be 0.20 s. Which of the following is true? ( a ) The wavelength of the wave is 5.0 m. ( b ) The frequency of the wave is 5.0 Hz. ( c ) The velocity of propagation of the wave is 5.0 m/s. ( d ) The wavelength of the wave is 0.20 m. ( e ) There is not enough information to justify any of these statements. Determine the Concept The distance between successive crests is one wavelength and the time between successive crests is the period of the wave motion. Thus, T = 0.20 s and f = 1/ T = 5.0 Hz. ) ( b is correct. 4 Two harmonic waves on identical strings differ only in amplitude. Wave A has an amplitude that is twice that of wave Bs. How do the energies of these waves compare? ( a ) E A = E B . ( b ) E A = 2 E B . ( c ) E A = 4 E B . ( d ) There is not enough information to compare their energies. Picture the Problem The average energy transmitted by a wave on a string is proportional to the square of its amplitude and is given by ( ) x A E 2 2 2 1 av = where A is the amplitude of the wave, is the linear density (mass per unit length) Chapter 15 1452 of the string, is the angular frequency of the wave, and x is the length of the string. Because the waves on the strings differ only in amplitude, the energy of the wave on string A is given by: 2 A A cA E = Express the energy of the wave on string B: 2 B B cA E = Divide the first of these equations by the second and simplify to obtain: 2 B A 2 B 2 A B A = = A A cA cA E E Because A A = 2 A B : 4 2 2 B B B A = = A A E E ( ) c is correct. 5 [SSM] To keep all of the lengths of the treble strings (unwrapped steel wires) in a piano all about the same order of magnitude, wires of different linear mass densities are employed. Explain how this allows a piano manufacturer to use wires with lengths that are the same order of magnitude....
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This note was uploaded on 01/29/2012 for the course PHYS 213 taught by Professor Oshea during the Fall '08 term at Kansas State University.
- Fall '08