Problem 16.1CYU: Check Your Understanding When a guitar string is plucked, the guitar string oscillates as a result... Problem 16.2CYU: Check Your Understanding The propagation velocity of a transverse or longitudinal mechanical wave... Problem 16.3CYU: Check Your Understanding The wave function above is derived using a sine function. Can a cosine... Problem 16.4CYU: Check Your Understanding The wave equation 2y(x,t)x2=1v22y(x,t)t2 works for any wave of the form... Problem 16.5CYU: Check Your Understanding The wave speed of a wave on a string depends on the tension and the linear... Problem 16.6CYU: Check Your Understanding Is the time-averaged power of a sinusoidal wave on a string proportional to... Problem 16.7CYU: Check Your Understanding The equations for the wavelengths and the frequencies of the modes of a... Problem 1CQ: Give one example of a transverse wave and one example of a longitudinal wave, being careful to note... Problem 2CQ: A sinusoidal transverse wave has a wavelength of 2.80 m. It takes 0.10 s for a portion of the string... Problem 3CQ: What is the difference between propagation speed and the frequency of a mechanical wave? Does one or... Problem 4CQ: Consider a stretched spring, such as a slinky. The stretched spring can support longitudinal waves... Problem 5CQ: Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does... Problem 6CQ: A sinusoidal, transverse wave is produced on a stretched spring, having a period T. Each section of... Problem 7CQ: An electromagnetic wave, such as light, does not require a medium. Can you think of an example that... Problem 8CQ: If you were to shake the end of a taut spring up and down 10 times a second, what would be the... Problem 9CQ: If you shake the end of a stretched spring up and down with a frequency f, you can produce a... Problem 10CQ: Does the vertical speed of a segment of a horizontal taut string through which a sinusoidal,... Problem 11CQ: In this section, we have considered waves that move at a constant wave speed. Does the medium... Problem 12CQ: If you drop a pebble in a pond you may notice that several concentric ripples are produced, not just... Problem 13CQ: If the tension in a string were increased by a factor of four, by what factor would the wave speed... Problem 14CQ: Does a sound wave move faster in seawater or fresh water, if both the sea water and fresh water are... Problem 15CQ: Guitars have strings of different linear mass density. If the lowest density string and the highest... Problem 16CQ: Shown below are three waves that were sent down a string at different times. The tension in the... Problem 17CQ: Electrical power lines connected by two utility poles are sometimes heard to hum when driven into... Problem 18CQ: Two strings, one with a low mass density and one with a high linear density are spliced together.... Problem 19CQ: Consider a string with under tension with a constant linear mass density. A sinusoidal wave with an... Problem 20CQ: Circular water waves decrease in amplitude as they move away from where a rock is dropped. Explain... Problem 21CQ: In a transverse wave on a string, the motion of the string is perpendicular to the motion of the... Problem 22CQ: The energy from the sun warms the portion of the earth facing the sun during the daylight hours. Why... Problem 23CQ: The intensity of a spherical waves decreases as the wave moves away from the source. If the... Problem 24CQ: An incident sinusoidal wave is sent along a string that is fixed to the wall with a wave speed of v.... Problem 25CQ: A string of a length of 2.00 m with a linear mass density of =0.006 kg/m is attached to the end of a... Problem 26CQ: A long, tight spring is held by two students, one student holding each end. Each student gives the... Problem 27CQ: Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is... Problem 28CQ: A string of a constant linear mass density is held taut by two students, each holding one end. The... Problem 29CQ: A truck manufacturer finds that a strut in the engine is failing prematurely. A sound engineer... Problem 30CQ: Why do roofs of gymnasiums and churches seem to fail more than family homes when an earthquake... Problem 31CQ: Wine glasses can be set into resonance by moistening your finger and rubbing it around the rim of... Problem 32CQ: Air conditioning units are sometimes placed on the roof of homes in the city. Occasionally, the air... Problem 33CQ: Consider a standing wave modeled as y(x,t)=4.00cmsin(3m1x)cos(4s1t) . Is there a node or an antinode... Problem 34P: Storms in the South Pacific can create waves that travel all the way to the California coast, 12,000... Problem 35P: Waves on a swimming pool propagate at 0.75 m/s. You splash the water at one end of the pool and... Problem 36P: Wind gusts create ripples on the ocean that have a wavelength of 5.00 cm and propagate at 2.00 m/s.... Problem 37P: How many times a minute does a boat bob up and down on ocean waves that have a wavelength of 40.0 m... Problem 38P: Scouts at a camp shake the rope bridge they have just crossed and observe the wave crests to be 8.00... Problem 39P: What is the wavelength of the waves you create in a swimming pool if you splash your hand at a rate... Problem 40P: What is the wavelength of an earthquake that shakes you with a frequency of 10.0 Hz and gets to... Problem 41P: Radio waves transmitted through empty space at the speed of light (v=c=3.00108m/s) by the Voyager... Problem 42P: Your ear is capable of differentiating sounds that arrive at each ear just 0.34 ms apart, which is... Problem 43P: (a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the... Problem 44P: A Girl Scout is taking a 10.00-km hike to earn a merit badge. While on the hike, she sees a cliff... Problem 45P: A quality assurance engineer at a frying pan company is asked to qualify a new line of... Problem 46P: A pulse can be described as a single wave disturbance that moves through a medium. Consider a pulse... Problem 47P: A transverse wave on a string is modeled with the wave function... Problem 48P: Consider the wave function y(x,t)=(3.00cm)sin(0.4m1x+2.00s1t+10) . What are the period, wavelength,... Problem 49P: A pulse is defined as y(x,t)=e2.77( 2.00( x2.00m/s ( t ) ) 5.00m)2 . Use a spreadsheet, or other... Problem 50P: A wave is modeled at time t=0.00s with a wave function that depends on position. The equation is... Problem 51P: A wave is modeled with the function y(x,t)=(0.25m)cos(0.30m1x0.90s1t+3) . Find the (a) amplitude,... Problem 52P: A surface ocean wave has an amplitude of 0.60 m and the distance from trough to trough is 8.00 m. It... Problem 53P: A wave is modeled by the wave function y(x,t)=(0.30m)sin[24.50m(x18.00mst)] . What are the... Problem 54P: A transverse wave on a string is described with the wave function y(x,t)=(0.50cm)sin(1.57m1x6.28s1t)... Problem 55P: A swimmer in the ocean observes one day that the ocean surface waves are periodic and resemble a... Problem 56P: Consider a wave described by the wave function y(x,t)=0.3msin(2.00m1x628.00s1t) . (a) How many... Problem 57P: Consider two waves defined by the wave functions y1(x,t)=0.50msin(23.00mx+24.00st) and... Problem 58P: Consider two waves defined by the wave functions y1(x,t)=0.20msin(26.00mx24.00st) and... Problem 59P: The speed of a transverse wave on a string is 300.00 m/s, its wavelength is 0.50 m, and the... Problem 60P: Transverse waves are sent along a 5.00-m-long string with a speed of 30.00 m/s. The string is under... Problem 61P: A copper wire has a density of =8920 kg/m3, a radius of 1.20 mm, and a length L. The wire is held... Problem 62P: A piano wire has a linear mass density of =4.95103 kg/m. Under what tension must the string be kept... Problem 63P: A string with a linear mass density of =0.0060 kg/m is tied to the ceiling. A 20-kg mass is tied to... Problem 64P: A cord has a linear mass density of =0.0075 kg/m and a length of three meters. The cord is plucked... Problem 65P: A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N... Problem 66P: Two strings are attached to poles, however the first string is twice as long as the second. If both... Problem 67P: Two strings are attached to poles, however the first string is twice the linear mass density mu of... Problem 68P: Transverse waves travel through a string where the tension equals 7.00 N with a speed of 20.00 m/s.... Problem 69P: Two strings are attached between two poles separated by a distance of 2.00 m as shown below, both... Problem 70P: Two strings are attached between two poles separated by a distance of 2.00 meters as shown in the... Problem 71P: The note E4 is played on a piano and has a frequency of f=393.88 . If the linear mass density of... Problem 72P: Two transverse waves travel through a taut string. The speed of each wave is v=30.00 m/s. A plot of... Problem 73P: A sinusoidal wave travels down a taut, horizontal string with a linear mass density of =0.060 kg/m .... Problem 74P: The speed of a transverse wave on a string is v=60.00 m/s and the tension in the string is FT=100.00... Problem 75P: A string of length 5 m and a mass of 90 g is held under a tension of 100 N. A wave travels down the... Problem 76P: Ultrasound of intensity 1.50102W/m2 is produced by the rectangular head of a medical imaging device... Problem 77P: The low-frequency speaker of a stereo set has asurface area of A=0.05 m2 and produces 1 W of... Problem 78P: To increase the intensity of a wave by a factor of 50, by what factor should the amplitude be... Problem 79P: A device called an insolation meter is used to measure the intensity of sunlight. It has an area of... Problem 80P: Energy from the Sun arrives at the top of Earth’s atmosphere with an intensity of 1400 W/m2. How... Problem 81P: Suppose you have a device that extracts energy from ocean breakers in direct proportion to their... Problem 82P: A photovoltaic array of (solar cells) is 10.0% efficient in gathering solar energy and converting it... Problem 83P: A microphone receiving a pure sound tone feeds an oscilloscope, producing a wave on its screen. If... Problem 84P: A string with a mass of 0.30 kg has a length of 4.00 m. If the tension in the string is 50.00 N, and... Problem 85P: The power versus time for a point on a string (=0.05kg/m) in which a sinusoidal traveling wave is... Problem 86P: A string is under tension FT1. Energy is transmitted by a wave on the string at rate P1by a wave of... Problem 87P: A 250-Hz tuning fork is struck and the intensity at the source is I1at a distance of one meter from... Problem 88P: A sound speaker is rated at a voltage of P=120.00 V and a current of I=10.00 A. Electrical power... Problem 89P: The energy of a ripple on a pond is proportional to the amplitude squared. If the amplitude of the... Problem 90P: Consider two sinusoidal waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x+3s1t) and... Problem 91P: Consider two sinusoidal sine waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x+3s1t+3)... Problem 92P: Consider two sinusoidal sine waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x3s1t)... Problem 93P: Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of... Problem 94P: Two sinusoidal waves are moving through a medium in the positive x-direction, both having amplitudes... Problem 95P: Two sinusoidal waves are moving through a medium in the positive x-direction, both having amplitudes... Problem 96P: Consider two waves y1(x,t) and y2(x,t) that are identical except for a phase shift propagating in... Problem 97P: Two sinusoidal waves, which are identical except for a phase shift, travel along in the same... Problem 98P: Two sinusoidal waves, which are identical except for a phase shift, travel along in the same... Problem 99P: Consider two wave functions, y1(x,t)=0.40msin(m1xs1t) and y2(x,t)=0.40msin(m1xs1t+3) . (a) Using a... Problem 100P: Consider two wave functions, y2(x,t)=2.00msin(2m1x3s1t) and y2(x,t)=2.00msin(2m1x3s1t+6) . (a)... Problem 101P: Consider two wave functions that differ only by a phase shift, y1(x,t)=Acos(kxt) and... Problem 102P: A wave traveling on a Slinky® that is stretched to 4 m takes 2.4 s to travel the length of the... Problem 103P: A 2-m long string is stretched between two supports with a tension that produces a wave speed equal... Problem 104P: Consider the experimental setup shown below. The length of the string between the string vibrator... Problem 105P: A cable with a linear density of =0.2 kg/m is hung from telephone poles. The tension in the cable is... Problem 106P: Consider a rod of length L, mounted in the center to a support. A node must exist where the rod is... Problem 107P: Consider two wave functions y(x,t)=0.30cmsin(3m1x4s1t) and y(x,t)=0.30cmsin(3m1x+4s1t) . Write a... Problem 108P: A 2.40-m wire has a mass of 7.50 g and is under a tension of 160 N. The wire is held rigidly at both... Problem 109P: A string with a linear mass density of 0.0062 kg/m and a length of 3.00 m is set into the n=4 mode... Problem 110P: A string with a linear mass density of 0.0075 kg/m and a length of 6.00 m is set into the n=4 mode... Problem 111P: Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a... Problem 112P: A string, fixed on both ends, is 5.00 m long and has a mass of 0.15 kg. The tension if the string is... Problem 113P: A string is fixed at both end. The mass of the string is 0.0090 kg and the length is 3.00 m. The... Problem 114P: The frequencies of two successive modes of standing waves on a string are 258.36 Hz and 301.42 Hz.... Problem 115P: A string is fixed at both ends to supports 3.50 m apart and has a linear mass density of =0.005... Problem 116P: Sine waves are sent down a 1.5-m-long string fixed at both ends. The waves reflect back in the... Problem 117AP: Ultrasound equipment used in the medical profession uses sound waves of a frequency above the range... Problem 118AP: Shown below is the plot of a wave function that models a wave at time t=0.00 s and t=2.00 s . The... Problem 119AP: The speed of light in air is approximately v=3.00108 m/s and the speed of light in glass is... Problem 120AP: A radio station broadcasts radio waves at a frequency of 101.7 MHz. The radio waves move through the... Problem 121AP: A sunbather stands waist deep in the ocean and observes that six crests of periodic surface waves... Problem 122AP: A tuning fork vibrates producing sound at a frequency of 512 Hz. The speed of sound of sound in air... Problem 123AP: A motorboat is traveling across a lake at a speed of vb=15.00 m/s. The boat bounces up and down... Problem 124AP: Use the linear wave equation to show that the wave speed of a wave modeled with the wave function... Problem 125AP: Given the wave functions y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kxt+) with 2 , show that y1(x,t)+y2(x,t)... Problem 126AP: A transverse wave on a string is modeled with the wave function... Problem 127AP: A sinusoidal wave travels down a taut, horizontal string with a linear mass density of =0.060 kg/m.... Problem 128AP: A transverse wave on a string (=0.0030kg/m) is described with the equation... Problem 129AP: A transverse wave on a horizontal string (=0.0060kg/m) is described with the equation... Problem 130AP: A student holds an inexpensive sonic range finder and uses the range finder to find the distance to... Problem 131AP: A wave on a string is driven by a string vibrator, which oscillates at a frequency of 100.00 Hz and... Problem 132AP: A traveling wave on a string is modeled by the wave equation y(x,t)=0.30msin(8.00m1x+100.00s1t) .... Problem 133AP: A transverse wave on a string has a wavelength of 5.0 m, a period of 0.02 s, and an amplitude of 1.5... Problem 134AP: (a) What is the intensity of a laser beam used to burn away cancerous tissue that, when 90.0%... Problem 135AP: Consider two periodic wave functions, y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kxt+) . (a) For what values... Problem 136AP: Consider two periodic wave functions, y1(x,t)=Asin(kxt) and y2(x,t)=Acos(kxt+) . (a) For what values... Problem 137AP: A trough with dimensions 10.00 meters by 0.10 meters by 0.10 meters is partially filled with water.... Problem 138AP: A seismograph records the S- and P-waves from an earthquake 20.00 s apart. If they traveled the same... Problem 139AP: Consider what is shown below. A 20.00-kg mass rests on a frictionless ramp inclined at 45° . A... Problem 140AP: Consider the superposition of three wave functions y(x,t)=3.00cmsin(2m1x3s1t) ,... Problem 141AP: A string has a mass of 150 g and a length of 3.4 m. One end of the string is fixed to a lab stand... Problem 142AP: A standing wave is produced on a string under a tension of 70.0 N by two sinusoidal transverse waves... Problem 143AP: A string with a length of 4 m is held under a constant tension. The string has a linear mass density... Problem 144CP: A copper wire has a radius of 200 µ m and a length of 5.0 m. The wire is placed under a tension of... Problem 145CP: A pulse moving along the x axis can be modeled as the wave function y(x,t)=4.00me( x+( 2.00m/s )t... Problem 146CP: A string with a linear mass density of =0.0085 kg/m is fixed at both ends. A 5.0-kg mass is hung... Problem 147CP: Consider two wave functions y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kx+t+) . What is the wave function... Problem 148CP: The wave function that models a standing wave is given as... Problem 149CP: Consider two wave functions y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kx+t+) . The resultant wave form when... format_list_bulleted
