HW9 full solution with detailsand steps pictures PDF

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HWNote: Since Mastering Physics randomizes numerical parameters, their values in this solutionmay be different from those you have for your homework assignment in Mastering Physics.Parameters in this solution follow those printed in the textbook.15 A 1-m-long uniform bar that weighs 628 N is suspend...

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HW9 Note: Since Mastering Physics randomizes numerical parameters, their values in this solution may be different from those you have for your homework assignment in Mastering Physics. Parameters in this solution follow those printed in the textbook. 15.57 A 1.80-m-long uniform bar that weighs 628 N is suspended in a horizontal position by two vertical wires that are attached to the ceiling. One wire is aluminum and the other is copper. The aluminum wire is attached to the left-hand end of the bar, and the copper wire is attached 0.400 m to the left of the right-hand end. Each wire has length 0.600 m and a circular cross section with radius 0.290 mm.

(a) What is the fundamental frequency of transverse standing waves for the aluminium wire? (b) What is the fundamental frequency of transverse standing waves for the copper wire?

15.62 A vibrating string 50.0 cm long is under a tension of 1.05 N. The results from five successive stroboscopic pictures are shown in the figure. The strobe rate is set at 5000 flashes per minute, and observations reveal that the maximum displacement occurred at flashes 1 and 5 with no other maxima in between.

(a) Find the period for the traveling waves on this string. (b) Find the frequency for the traveling waves on this string. (c) Find the wavelength for the traveling waves on this string. (d) In what harmonic is the string vibrating?

(e) What is the speed of the traveling waves on the string? (f) How fast is point P moving when the string is in position 1? (g) How fast is point P moving when the string is in position 3? (h) What is the mass of this string?

16.39 A violinist is tuning her instrument to concert A (440 Hz). She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat of frequency 3.00 Hz, which increases to 4.00 Hz when she tightens her violin string slightly. (a) What was the frequency of her violin when she heard the 3.00 Hz beat? (b) To get her violin perfectly tuned to concert A, should she tighten or loosen her string from what it was when she heard the 3.00 Hz beat?

16.45 A swimming duck paddles the water with its feet once per time interval of 1.4 s, producing surface waves with this period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.37 m/s, and the crests of the waves ahead of the duck have a spacing of 0.19 m.

(a) What is the duck's speed? (b) How far apart are the crests behind the duck?

16.50 The siren of a fire engine that is driving northward at 37.0 m/s emits a sound of frequency 2040 Hz. A truck in front of this fire engine is moving northward at 21.0 m/s.

(a) What is the frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck? (b) What wavelength would this driver measure for these reflected sound waves?

16.58 A uniform 165 N bar is supported horizontally by two identical wires A and B. A small 185 N cube of lead is placed three-fourths of the way from A to B. The wires are each 75.0 cm long and have a mass of 5.50 g.

If both of them are simultaneously plucked at the center, what is the frequency of the beats that they will produce when vibrating in their fundamental?

15.22 A piano wire with mass 3.25 g and length 77.0 cm is stretched with a tension of 27.0 N. A wave with frequency 120 Hz and amplitude 1.20 mm travels along the wire. (a) Calculate the average power carried by the wave. (b) What happens to the average power if the wave amplitude is halved?

15.7 Transverse waves on a string have wave speed v = 8.00 m/s, amplitude A = 0.0700 m, and wavelength λ = 0.320 m. The waves travel in the -xx direction, and at t = 0 the x = 0 end of the string has its maximum upward displacement. For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of Wave on a clothesline.

(a) Find the frequency of these waves. (b) Find the period of these waves. (c) Find the wave number of these waves. (d) Write a wave function describing the wave. (e) Find the transverse displacement of a particle at x = 0.360 m at time t = 0.150 s. (f) How much time must elapse from the instant in part E until the particle at x = 0.360 m next has maximum upward displacement?

15.34 Adjacent antinodes of a standing wave on a string are 15.0 cm apart. A particle at an antinode oscillates in simple harmonic motion with amplitude 0.850 cm and period 0.0750 s. The string lies along the +x-axis and is fixed at x = 0. (a) How far apart are the adjacent nodes?

(b) What is the wavelength of the two traveling waves that form this pattern? (c) What is the amplitude of the two traveling waves that form this pattern? (d) What is the speed of the two traveling waves that form this pattern?

(e) Find the maximum and minimum transverse speeds of a point at an antinode. (f) What is the shortest distance along the string between a node and an antinode?

A transverse wave on a 15.46 (0.750cm)cos(π[(0.400cm−1)x+(250s−1)t]).

rope

is

given

(a) Find the amplitude. (b) Find the period. (c) Find the frequency. (d) Find the wavelength. (e) Find the speed of propagation. (f) Is the wave traveling in the +x- or -x-direction? (g) The mass per unit length of the rope is 0.0500 kg/m. Find the tension. (h) Find the average power of this wave.

by y(x,t)

=

16.59 An organ pipe has two successive harmonics with frequencies 1372 and 1764 Hz. (a) Is this an open or a stopped pipe? (b) What two harmonics are these? (c) What is the length of the pipe?

16.62 A bat flies toward a wall, emitting a steady sound of frequency 1.70 kHz. This bat hears its own sound plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency of 8.00 Hz?...