Fundamentals of Physics Extended 9th Edition solutions

Fundamentals of Physics Extended 9
The following four waves are sent along strings with the same linear densities (x is in meters and t is in seconds). Rank the waves according to (a) their wave speed and (b) the tension in the strings along which they travel, greatest first: (1) Yl = (3 mm) sin(x - 3t), (3) )'3 = (1 mm) sin(4x - t),

Fundamentals of Physics Extended 9
In Fig. 16-23, wave 1 consists of a rectangular peak of height 4 units and width d, and a rectangular valley of depth 2 units and width d. The wave travels rightward along an x axis. Choices 2, 3, and 4 are similar waves, with the same heights, depths, and widths, that will travel leftward along that

Fundamentals of Physics Extended 9
Figure 16-24a gives a snapshot of a wave traveling in the direction of positive x along a string under tension. Four string elements are indicated by the lettered points. For each of those elements, determine whether, at the instant of the snapshot, the element is moving upward or downward or is mome

Fundamentals of Physics Extended 9
Figure 16-25 shows three waves that are separately sent along a string that is stretched under a certain tension along an x axis. Rank the waves according to their (a) wavelengths, (b) speeds, and (c) angular frequencies, greatest first.

Fundamentals of Physics Extended 9
If you start with two sinusoidal waves of the same amplitude traveling in phase on a string and then somehow phase-shift one of them by 5.4 wavelengths, what type of interference will occur on the string?

Fundamentals of Physics Extended 9
The amplitudes and phase differences for four pairs of waves of equal wavelengths are (a) 2 mm, 6 mm, and 7Trad; (b) 3 mm, 5 mm, and 7Trad; (c) 7 mm, 9 mm, and 7Trad; (d) 2 mm, 2 QUESTIONS 437 mrn, and 0 rad. Each pair travels in the same direction along the same string. Without written calculation,

Fundamentals of Physics Extended 9
A sinusoidal wave is sent along a cord under tension, transporting energy at the average rate of Pavg,l' Two waves, identical to that first one, are then to be sent along the cord with a phase difference of either 0, 0.2 wavelength, or 0.5 wavelength. (a) With only mental calculation, rank those cho

Fundamentals of Physics Extended 9
(a) If a standing wave on a string is given by y'(t) = (3 mm) sin(5x) cos(4t), is there a node or an antinode of the oscillations of the string at x = O? (b) If the standing wave is given by y'(t) = (3 mm) sin(5x + 7T/2) cos(4t), is there a node or an antinode at x = O?

Fundamentals of Physics Extended 9
Strings A and B have identical lengths and linear densities, but string B is under greater tension than string A. Figure 16-26 shows four situations, (a) through (d), in which standing wave patterns exist on the two strings. In which situations is there the possibility that strings A and B are oscill

Fundamentals of Physics Extended 9
If you set up the seventh harmonic on a string, (a) how many nodes are present, and (b) is there a node, antinode, or some intermediate state at the midpoint? If you next set up the sixth harmonic, (c) is its resonant wavelength longer or shorter than that for the seventh harmonic, and (d) is the res

Fundamentals of Physics Extended 9
Figure 16-27 shows phasor diagrams for three situations in which two waves travel along the same string. All six waves have the same amplitude. Rank the situations according to the amplitude of the net wave on the string, greatest first.

Fundamentals of Physics Extended 9
The function y(x, t) = (15.0 cm) cos( 1TX - 15771), with x in meters and t in seconds, describes a wave on a taut string. What is the transverse speed for a point on the string at an instant when that point has the displacement Y = + 12.0 cm?

Fundamentals of Physics Extended 9
A sinusoidal wave of frequency 500 Hz has a speed of 350 m/s. (a) How far apart are two points that differ in phase by 1T/3 rad? (b) What is the phase difference between two displacements at a certain point at times 1.00 ms apart?

Fundamentals of Physics Extended 9
The equation of a transverse wave on a string is Y = (2.0 mm) sin[(20 m-1)x - (600 S-l)t]. The tension in the string is 15 N. (a) What is the wave speed? (b) Find the linear density of this string in grams per meter.

Fundamentals of Physics Extended 9
A stretched string has a mass per unit length of 5.00 g/cm and a tension of 10.0 N. A sinusoidal wave on this string has an amplitude of 0.12 mm and a frequency of 100 Hz and is traveling in the negative direction of an x axis. If the wave equation is of the form y(x, t) = YIIl sin(kx ::':: wt), what

Fundamentals of Physics Extended 9
The speed of a transverse wave on a string is 170 m/s when the string tension is 120 N. To what value must the tension be changed to raise the wave speed to 180 rnfs?

Fundamentals of Physics Extended 9
The linear density of a string is 1.6 X 10-4 kg/m. A transverse wave on the string is described by the equation Y = (0.021 m) sin[(2.0 m-1)x + (30 S-l)t]. What are (a) the wave speed and (b) the tension in the string?

Fundamentals of Physics Extended 9
The heaviest and lightest strings on a certain violin have linear densities of 3.0 and 0.29 g/m. What is the ratio of the diameter of the heaviest string to that of the lightest string, assuming that the strings are of the same material?

Fundamentals of Physics Extended 9
What is the speed of a transverse wave in a rope of length 2.00 m and mass 60.0 g under a tension of 500 N?

Fundamentals of Physics Extended 9
The tension in a wire clamped at both ends is doubled without appreciably changing the wire's length between the clamps. What is the ratio of the new to the old wave speed for transverse waves traveling along this wire?

Fundamentals of Physics Extended 9
A 100 g wire is held under a tension of 250 N with one end at x = 0 and the other at x = 10.0 m. At time t = 0, pulse 1 is sent along the wire from the end at x = 10.0 m. At time t = 30.0 ms, pulse 2 is sent along the wire from the end at x = O. At what position x do the pulses begin to meet?

Fundamentals of Physics Extended 9
A sinusoidal wave is traveling on a string with speed 40 cm/s. The displacement of the particles of the string at x = 10 cm varies with time according to Y = (5.0 cm) sin[1.0 - (4.0 S-l)t]. The linear density of the string is 4.0 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If

Fundamentals of Physics Extended 9
A sinusoidal trans- y (em) verse wave is traveling along a string in the negative direction of an x axis. Figure 16-34 shows a plot of the displacement as a function of position at time t = 0; the scale of the Y axis is set by Ys = 4.0 cm. The string tension is 3.6 N, and its linear density is 25 g/m

Fundamentals of Physics Extended 9
In Fig. 16-35a, string 1 has a linear density of 3.00 g/m, and string 2 has a linear density of 5.00 g/m. They are under tension due to the hanging block of mass M = 500 g. Calculate the wave speed on (a) string 1 and (b) string 2. (Hint: When a string loops halfway around a pulley, it pulls on the p

Fundamentals of Physics Extended 9
A uniform rope of mass m Fig. 16-35 Problem 24. and length L hangs from a ceiling. (a) Show that the speed of a transverse wave on the rope is a function of Y, the distance from the lower end, and is given by v = vgy. (b) Show that the time a transverse wave takes to travel the length of the rope is

Fundamentals of Physics Extended 9
A string along which waves can travel is 2.70 m long and has a mass of 260 g. The tension in the string is 36.0 N. What must be the frequency of traveling waves of amplitude 7.70 mm for the average power to be 85.0 W?

Fundamentals of Physics Extended 9
A sinusoidal wave is sent along a string with a linear density of 2.0 g/m. As it travels, the kinetic energies of the mass elements along the string vary. Figure 16-36a gives the rate dKldt at which kinetic energy passes through the string elements at a particular instant, plotted as a function of di

Fundamentals of Physics Extended 9
Use the wave equation to find the speed of a wave given by y(x, t) = (3.00 mm) sin[( 4.00 m-I)x - (7.00 S-I)t].

Fundamentals of Physics Extended 9
Use the wave equation to find the speed of a wave given by y(x, t) = (2.00 mm)[(20 m-I)x - (4.0 S-I)t]O.5.

Fundamentals of Physics Extended 9
Use the wave equation to find the speed of a wave given in terms of the general function hex, t): y(x, t) = (4.00 mm) h[(30 m-I)x + (6.0 S-I)t].

Fundamentals of Physics Extended 9
Two identical traveling waves, moving in the same direction, are out of phase by 1T12 rad. What is the amplitude of the resultant wave in terms of the common amplitude Ym of the two combining waves?

Fundamentals of Physics Extended 9
What phase difference between two identical traveling waves, moving in the same direction along a stretched string, results in the combined wave having an amplitude 1.50 times that of the common amplitude of the two combining waves? Express your answer in (a) degrees, (b) radians, and (c) wavelengths

Fundamentals of Physics Extended 9
Two sinusoidal waves with the same amplitude of 9.00 mm and the same wavelength travel together along a string that is stretched along an x axis. Their resultant wave is shown twice in Fig. 16-37, as valley A travels in the negative direction of the x axis by distance d = 56.0 cm in 8.0 ms. The tick

Fundamentals of Physics Extended 9
A sinusoidal wave of angular frequency 1200 rad/s and amplitude 3.00 mm is sent along a cord with linear density 2.00 g/m and tension 1200 N. (a) What is the average rate at which energy is transported by the wave to the opposite end of the cord? (b) If, simultaneously, an identical wave travels alon

Fundamentals of Physics Extended 9
Two sinusoidal waves of the same frequency travel in the same direction along a string. If YlIll = 3.0 cm, YIIl2 = 4.0 cm, 4>1 = 0, and 2 = 1T12 rad, what is the amplitude of the resultant wave?

Fundamentals of Physics Extended 9
Four waves are to be sent along the same string, in the same direction: YI (x, t) = (4.00 mm) sin(21Tx - 4001Tt) Y2(X, t) = (4.00 mm) sin(21Tx - 4001Tt + 0.71T) Y3(X, t) = (4.00 mm) sin(21Tx - 4001Tt + 1T) Y4(X, t) = (4.00 mm) sin(21Tx - 4001Tt + 1.71T). What is the amplitude of the resultant wave?

Fundamentals of Physics Extended 9
These two waves travel along the same string: Yl (x, t) = (4.60 mm) sin(21Tx - 4001Tt) heX, t) = (5.60 mm) sin(21Tx - 4001Tt + 0.801Trad). What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.00 mm is also to be sent along t

Fundamentals of Physics Extended 9
Two sinusoidal waves of the same frequency are to be sent in the same direction along a taut string. One wave has an amplitude of 5.0 mm, the other 8.0 mm. (a) What phase difference 4>l between the two waves results in the smallest amplitude of the resultant wave? (b) What is that smallest amplitude?

Fundamentals of Physics Extended 9
Two sinusoidal waves of the same period, with amplitudes of 5.0 and 7.0 mm, travel in the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.0 mm. The phase constant of the 5.0 mm wave is O. What is the phase constant of the 7.0 mm wave?

Fundamentals of Physics Extended 9
Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string with a speed of 10 cm/s. If the time interval between instants when the string is flat is 0.50 s, what is the wavelength of the waves?

Fundamentals of Physics Extended 9
A string fixed at both ends is 8.40 m long and has a mass of 0.120 kg. It is subjected to a tension of 96.0 N and set oscillating. (a) What is the speed of the waves on the string? (b) What is the longest possible wavelength for a standing wave? (c) Give the frequency of that wave.

Fundamentals of Physics Extended 9
A string under tension Ti oscillates in the third harmonic at frequency /3, and the waves on the string have wavelength A3 If the tension is increased to T! = 47) and the string is again made to oscillate in the third harmonic, what then are (a) the frequency of oscillation in terms of /3 and (b) the

Fundamentals of Physics Extended 9
What are (a) the lowest frequency, (b) the second lowest frequency, and (c) the third lowest frequency for standing waves on a wire that is 10.0 m long, has a mass of 100 g, and is stretched under a tension of 250 N?

Fundamentals of Physics Extended 9
A 125 cm length of string has mass 2.00 g and tension 7.00 N. (a) What is the wave speed for this string? (b) What is the lowest resonant frequency of this string?

Fundamentals of Physics Extended 9
A string that is stretched between fixed supports separated by 75.0 cm has resonant frequencies of 420 and 315 Hz, with no intermediate resonant frequencies. What are (a) the lowest resonant frequency and (b) the wave speed?

Fundamentals of Physics Extended 9
String A is stretched between two clamps separated by distance L. String B, with the same linear density and under the same tension as string A, is stretched between two clamps separated by distance 4L. Consider the first eight harmonics of string B. For which of these eight harmonics of B (if any) d

Fundamentals of Physics Extended 9
One of the harmonic frequencies for a particular string under tension is 325 Hz. The next higher harmonic frequency is 390 Hz. What harmonic frequency is next higher after the harmonic frequency 195 Hz?

Fundamentals of Physics Extended 9
If a transmission line in a cold climate collects ice, the increased diameter tends to cause vortex formation in a passing wind. The air pressure variations in the vortexes tend to cause the line to oscillate (gallop), especially if the frequency of the variations matches a resonant frequency of the

Fundamentals of Physics Extended 9
A nylon guitar string has a linear density of 7.20 g/m and is under a tension of 150 N. The fixed supports are distance D = 90.0 cm apart. The string is oscillating in the standing Fig. 16-38 Problem 49. wave pattern shown in Fig. 16-38. Calculate the (a) speed, (b) wavelength, and (c) frequency of t

Fundamentals of Physics Extended 9
For a certain transverse standing wave on a long string, an antinode is at x = 0 and an adjacent node is at x = 0.10 m. The displacement yet) of the string particle at x = 0 is shown in Fig. 16-39, where the scale of the y axis is set by Ys = 4.0 cm. When t = 0.50 s, what is S the displacement of the

Fundamentals of Physics Extended 9
Two waves are generated on a string of length 3.0 m to produce a three-loop standing wave with an amplitude of 1.0 cm. The wave speed is 100 m/s. Let the equation for one of the waves be of the form y(x, t) = YIIl sin(kx + wt). In the equation for the other wave, what are (a) YIII' (b) k, (c) w, and

Fundamentals of Physics Extended 9
A rope, under a tension of 200 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by Y = (0.10 m)(sin m:12) sin 121Tt, where x = 0 at one end of the rope, x is in meters, and t is in seconds. What are (a) the length of the rope, (b)

Fundamentals of Physics Extended 9
A string oscillates according to the equation Y' = (0.50 cm) sin[ ( ; cm-1)x J cOS[(401TS-1)t]. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the tran

Fundamentals of Physics Extended 9
Two sinusoidal waves with the same amplitude and wavelength travel through each other along a string that is stretched along an x axis. Their resultant wave is shown twice in Fig. 16-40, as the antinode A travels from an extreme upward displacement to an extreme downward displacement in 6.0 ms. The t

Fundamentals of Physics Extended 9
The following two waves are sent in opposite directions on a horizontal string so as to create a standing wave in a vertical plane: Yl(X, t) = (6.00 mm) sin(4.00m: - 4001Tf) Yz(x, t) = (6.00 mm) sin(4.00m: + 4001Tf), with x in meters and t in seconds. An antinode is located at point A. In the time in

Fundamentals of Physics Extended 9
A standing wave pattern on a string is described by y(x, t) = 0.040 (sin 51Tx)(cos 401Tt), where x and yare in meters and t is in seconds. For x 2: 0, what is the location of the node with the (a) smallest, (b) second smallest, and ( c) third smallest value of x? (d) What is the period of the oscilla

Fundamentals of Physics Extended 9
A generator at one end of a very long string creates a wave given by 1T Y = (6.0 cm) cos 2 [(2.00 m-1)x + (8.00 S-l)t], and a generator at the other end creates the wave Y = (6.0 cm) cos ; [(2.00 m-1)x - (8.00 S-l)t]. Calculate the (a) frequency, (b) wavelength, and (c) speed of each wave. For x 2: 0

Fundamentals of Physics Extended 9
In Fig. 16-41, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 1.20 m, linear density f.L = 1.6 glm, and the oscillator frequency f = 120 Hz. The amplitude of the motion at P is small enough for that point to be conside

Fundamentals of Physics Extended 9
In Fig. 16-42, an aluminum wire, of length Ll = 60.0 cm, cross-sectional area 1.00 X 10-2 cm2, and density 2.60 g/cm3, is joined to a steel wire, of density 7.80 g/cm3 and the same cross-sectional area. The compound wire, loaded with a block of mass m = 10.0 kg, is arranged so that the distance L2 fr

Fundamentals of Physics Extended 9
In Fig. 16-41, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. The separation L between P and Q is 1.20 m, and the frequency f of the oscillator is fixed at 120 Hz. The amplitude of the motion at P is small enough for that point to be

Fundamentals of Physics Extended 9
In an experiment on standing waves, a string 90 cm long is attached to the prong of an electrically driven tuning fork that oscillates perpendicular to the length of the string at a frequency of 60 Hz. The mass of the string is 0.044 kg. What tension must the string be under (weights are attached to

Fundamentals of Physics Extended 9
A sinusoidal transverse wave traveling in the positive direction of an x axis has an amplitude of 2.0 cm, a wavelength of 10 cm, and a frequency of 400 Hz. If the wave equation is of the form y(x, t) = Ym sin(kx wt), what are (a) Ym' (b) k, (c) w, and (d) the correct choice of sign in front of w? Wh

Fundamentals of Physics Extended 9
A wave has a speed of 240 mls and a wavelength of 3.2 ill. What are the (a) frequency and (b) period of the wave?

Fundamentals of Physics Extended 9
The equation of a transverse wave traveling along a string is Y = 0.15 sin(0.79x - 13t), in which x and yare in meters and t is in seconds. (a) What is the displacement Y at x = 2.3 m, t = 0.16 s? A second wave is to be added to the first wave to produce standing waves on the string. If the wave equa

Fundamentals of Physics Extended 9
The equation of a transverse wave traveling along a string is Y = (2.0 mm) sin[(20 m-l)x - (600 S-l)t]. Find the (a) amplitude, (b) frequency, (c) velocity (including sign), and (d) wavelength of the wave. (e) Find the maximum transverse speed of a particle in the string.

Fundamentals of Physics Extended 9
Figure 16-43 shows the displacement Y versus time t of the point on a string at x = 0, as a wave passes through that point. The scale of the Y axis is set by Ys = 6.0 mrn. The wave is given by y(x, t) = YIIl sin(la: - wt + ). What is ? (Caution: A calculator does not always give the proper y(mm) ~, -

Fundamentals of Physics Extended 9
Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave y' (x, t) = (3.0 mm) sin(20x - 4.0t + 0.820 rad), with x in meters and t in seconds. What are (a) the wavelength A of the two waves, (b) the phase difference between them, and (c) the

Fundamentals of Physics Extended 9
A single pulse, given by h(x - 5.0t), is shown in Fig. 16-44 for t = O. The scale of the vertical axis is set by hs = 2. Here x is in centimeters and t is in seconds. " ~ What are the (a) speed and (b) dix rection of travel of the pulse? (c) Plot h(x - 5t) as a function of x for t = 2 s. (d) Plot h(x

Fundamentals of Physics Extended 9
Three sinusoidal waves of the same frequency travel along a string in the positive direction of an x axis. Their amplitudes are Yl> y1/2, and y 1/3, and their phase constants are 0, 7T/2, and 7T, respectively. What are the (a) amplitude and (b) phase constant of the resultant wave? (c) Plot the wave

Fundamentals of Physics Extended 9
Figure 16-45 shows transverse acceleration ay versus time t of the point on a string at x = 0, as a wave in the form of y(x, t) = Ym sin(kx - wt + ) passes through that point. The scale of the vertical axis is set by as = 400 mls2 What is ? (Caution: A calculator does not always give the proper inver

Fundamentals of Physics Extended 9
A transverse sinusoidal wave is generated at one end of a long, horizontal string by a bar that moves up and down through a distance of 1.00 cm. The motion is continuous and is repeated regularly 120 times per second. The string has linear density 120 glm and is kept under a tension of 90.0 N. Find t

Fundamentals of Physics Extended 9
Two sinusoidal 120 Hz waves, of the same frequency and amplitude, are to be sent in the positive direction of an x axis that is directed along a cord under tension. The waves can be s )" s s 0 1-------'1<-----1 sent in phase, or they can be Shift distance (cm) phase-shifted. Figure 16-46 shows Fig. 1

Fundamentals of Physics Extended 9
At time t = 0 and at position x = 0 m along a string, a traveling sinusoidal wave with an angular frequency of 440 rad/s has displacement Y = +4.5 mm and transverse velocity u = -0.75 m/s. If the wave has the general form y(x, t) = YII/ sin(kx - wt + ), what is phase constant ?

Fundamentals of Physics Extended 9
Energy is transmitted at rate PI by a wave of frequency fl on a string under tension 71' What is the new energy transmission rate P2 in terms of PI (a) if the tension is increased to 72 = 471 and (b) if, instead, the frequency is decreased to 12 = fIl2?

Fundamentals of Physics Extended 9
(a) What is the fastest transverse wave that can be sent along a steel wire? For safety reasons, the maximum tensile stress to which steel wires should be subjected is 7.00 X 108 N/m2 The density of steel is 7800 kg/m3. (b) Does your answer depend on the diameter of the wire?

Fundamentals of Physics Extended 9
A standing wave results from the sum of two transverse traveling waves given by YI = 0.050 cos( 1TX 41Tt) and Y2 = 0.050 cos( 1TX + 4171), where x, YI> and Y2 are in meters and t is in seconds. (a) What is the smallest positive value of x that corresponds to a node? Beginning at t = 0, what is the va

Fundamentals of Physics Extended 9
The type of rubber band used inside some baseballs and golf balls obeys Hooke's law over a wide range of elongation of the band. A segment of this material has an unstretched length e and a mass m. When a force Fis applied, the band stretches an additional PROBLEMS 443 length ile. (a) What is the spe

Fundamentals of Physics Extended 9
The speed of electromagnetic waves (which include visible light, radio, and x rays) in vacuum is 3.0 X 108 m/s. (a) Wavelengths of visible light waves range from about 400 nm in the violet to about 700 nm in the red. What is the range of frequencies of these waves? (b) The range of frequencies for sh

Fundamentals of Physics Extended 9
ALSO m wire has a mass of 8.70 g and is under a tension of 120 N. The wire is held rigidly at both ends and set into oscillation. (a) What is the speed of waves on the wire? What is the wavelength of the waves that produce (b) one-loop and (c) twoloop standing waves? What is the frequency of the wave

Fundamentals of Physics Extended 9
When played in a certain manner, the lowest resonant frequency of a certain violin string is concert A (440 Hz). What is the frequency of the (a) second and (b) third harmonic of the string?

Fundamentals of Physics Extended 9
A sinusoidal transverse wave traveling in the negative direction of an x axis has an amplitude of 1.00 cm, a frequency of 550 Hz, and a speed of 330 mls. If the wave equation is of the form y(x, t) = Ym sin(kx wt), what are (a) YII/' (b) w, (c) k, and (d) the correct choice of sign in front of w?

Fundamentals of Physics Extended 9
Two sinusoidal waves of the same wavelength travel in the same direction along a stretched string. For wave 1, YII/ = 3.0 mm and = 0; for wave 2, Ym = 5.0 mm and = 70. What are the (a) amplitude and (b) phase constant of the resultant wave?

Fundamentals of Physics Extended 9
A sinusoidal transverse wave of amplitude Ym and wavelength ;\ travels on a stretched cord. (a) Find the ratio of the maximum particle speed (the speed with which a single particle in the cord moves transverse to the wave) to the wave speed. (b) Does this ratio depend on the material of which the cor

Fundamentals of Physics Extended 9
Oscillation of a 600 Hz tuning fork sets up standing waves in a string clamped at both ends. The wave speed for the string is 400 mls. The standing wave has four loops and an amplitude of 2.0 mm. (a) What is the length of the string? (b) Write an equation for the displacement of the string as a funct

Fundamentals of Physics Extended 9
A 120 cm length of string is stretched between fixed supports. What are the (a) longest, (b) second longest, and (c) third longest wavelength for waves traveling on the string if standing waves are to be set up? (d) Sketch those standing waves.

Fundamentals of Physics Extended 9
(a) Write an equation describing a sinusoidal transverse wave traveling on a cord in the positive direction of a y axis with an angular wave number of 60 cm-I , a period of 0.20 s, and an amplitude of 3.0 mm. Take the transverse direction to be the z direction. (b) What is the maximum transverse spee

Fundamentals of Physics Extended 9
A wave on a string is described by y(x, t) = 15.0 sine 1Tx/8 - 4171), where x and yare in centimeters and t is in seconds. (a) What is the transverse speed for a point on the string at x = 6.00 cm when t = 0.250 s? (b) What is the maximum transverse speed of any point on the string? (c) What is the m

Fundamentals of Physics Extended 9
Body armor. When a high-speed projectile such as a bullet or bomb fragment strikes modern body armor, the fabric of the armor stops the projectile and prevents penetration by quickly spreading the projectile's energy over a large area. This spreading is done by longitudinal and transverse pulses that

Fundamentals of Physics Extended 9
Two waves are described by Yl = 0.30 sin[ 7T(5x 200)t] and Y2 = 0.30 sin[ 7T(5x - 200t) + 1T/3], where Yb Yz, and x are in meters and t is in seconds. When these two waves are combined, a traveling wave is produced. What are the (a) amplitude, (b) wave speed, and (c) wavelength of that traveling wave

Fundamentals of Physics Extended 9
A certain transverse sinusoidal wave of wavelength 20 cm is moving in the positive direction of an x axis. The transverse velocity of the particle at x = 0 as a function of time is shown in Fig. 1 6-48 Problem 90. Fig. 16-48, where the scale of the vertical axis is set by Us = 5.0 cm/s. What are the

Fundamentals of Physics Extended 9
In a demonstration, a 1.2 kg horizontal rope is fixed in place at its two ends (x = 0 and x = 2.0 m) and made to oscillate up and down in the fundamental mode, at frequency 5.0 Hz. At t = 0, the point at x = 1.0 m has zero displacement and is moving upward in the positive direction of a Y axis with a

Fundamentals of Physics Extended 9
Two waves, Yl = (2.50 mm) sin[(25.1 rad/m)x - (440 rad/s)t] and Y2 = (1.50 mm) sin[(25.1 rad/m)x + (440 rad/s)t], travel along a stretched string. (a) Plot the resultant wave as a function of t for x = 0, A/8, Al4, 3A18, and A12, where A is the wavelength. The graphs should extend from t = 0 to a lit

Fundamentals of Physics Extended 9
A traveling wave on a string is described by Y = 2.0 sin[ 21T( O.~O + ~~) J where x and yare in centimeters and t is in seconds. (a) For t = 0, plot Y as a function ofx for 0::; x::; 160 cm. (b) Repeat (a) for t = 0.05 sand t = 0.10 s. From your graphs, determine (c) the wave speed and (d) the direct