University Physics Volume 1
1st Edition
ISBN: 9781630182137
Author: Samuel J Ling Jeff, Sanny, William Moebs
Publisher: OpenStax
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Textbook Question
Chapter 16, Problem 31CQ
Wine glasses can be set into resonance by moistening your finger and rubbing it around the rim of the glass. Why?
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8.114 CALC A Variable-Mass Raindrop. In a rocket-propul-
sion problem the mass is variable. Another such problem is a rain-
drop falling through a cloud of small water droplets. Some of these
small droplets adhere to the raindrop, thereby increasing its mass
as it falls. The force on the raindrop is
dp
dv
dm
Fext
=
+
dt
dt
dt
=
Suppose the mass of the raindrop depends on the distance x that it
has fallen. Then m kx, where k is a constant, and dm/dt = kv.
This gives, since Fext
=
mg,
dv
mg = m
+ v(kv)
dt
Or, dividing by k,
dv
xgx
+ v²
dt
This is a differential equation that has a solution of the form
v = at, where a is the acceleration and is constant. Take the initial
velocity of the raindrop to be zero. (a) Using the proposed solution
for v, find the acceleration a. (b) Find the distance the raindrop has
fallen in t = 3.00 s. (c) Given that k = 2.00 g/m, find the mass of
the raindrop at t = 3.00 s. (For many more intriguing aspects of
this problem, see K. S. Krane, American Journal of…
8.13 A 2.00-kg stone is sliding Figure E8.13
F (kN)
to the right on a frictionless hori-
zontal surface at 5.00 m/s when
it is suddenly struck by an object
that exerts a large horizontal
force on it for a short period of 2.50
time. The graph in Fig. E8.13
shows the magnitude of this force
as a function of time. (a) What
impulse does this force exert on
t (ms)
15.0
16.0
the stone? (b) Just after the force stops acting, find the magnitude
and direction of the stone's velocity if the force acts (i) to the right
or (ii) to the left.
Please calculate the expectation value for E and the uncertainty in E for this wavefunction trapped in a simple harmonic oscillator potential
Chapter 16 Solutions
University Physics Volume 1
Ch. 16 - Check Your Understanding When a guitar string is...Ch. 16 - Check Your Understanding The propagation velocity...Ch. 16 - Check Your Understanding The wave function above...Ch. 16 - Check Your Understanding The wave equation...Ch. 16 - Check Your Understanding The wave speed of a wave...Ch. 16 - Check Your Understanding Is the time-averaged...Ch. 16 - Check Your Understanding The equations for the...Ch. 16 - Give one example of a transverse wave and one...Ch. 16 - A sinusoidal transverse wave has a wavelength of...Ch. 16 - What is the difference between propagation speed...
Ch. 16 - Consider a stretched spring, such as a slinky. The...Ch. 16 - Consider a wave produced on a stretched spring by...Ch. 16 - A sinusoidal, transverse wave is produced on a...Ch. 16 - An electromagnetic wave, such as light, does not...Ch. 16 - If you were to shake the end of a taut spring up...Ch. 16 - If you shake the end of a stretched spring up and...Ch. 16 - Does the vertical speed of a segment of a...Ch. 16 - In this section, we have considered waves that...Ch. 16 - If you drop a pebble in a pond you may notice that...Ch. 16 - If the tension in a string were increased by a...Ch. 16 - Does a sound wave move faster in seawater or fresh...Ch. 16 - Guitars have strings of different linear mass...Ch. 16 - Shown below are three waves that were sent down a...Ch. 16 - Electrical power lines connected by two utility...Ch. 16 - Two strings, one with a low mass density and one...Ch. 16 - Consider a string with under tension with a...Ch. 16 - Circular water waves decrease in amplitude as they...Ch. 16 - In a transverse wave on a string, the motion of...Ch. 16 - The energy from the sun warms the portion of the...Ch. 16 - The intensity of a spherical waves decreases as...Ch. 16 - An incident sinusoidal wave is sent along a string...Ch. 16 - A string of a length of 2.00 m with a linear mass...Ch. 16 - A long, tight spring is held by two students, one...Ch. 16 - Many of the topics discussed in this chapter are...Ch. 16 - A string of a constant linear mass density is held...Ch. 16 - A truck manufacturer finds that a strut in the...Ch. 16 - Why do roofs of gymnasiums and churches seem to...Ch. 16 - Wine glasses can be set into resonance by...Ch. 16 - Air conditioning units are sometimes placed on the...Ch. 16 - Consider a standing wave modeled as...Ch. 16 - Storms in the South Pacific can create waves that...Ch. 16 - Waves on a swimming pool propagate at 0.75 m/s....Ch. 16 - Wind gusts create ripples on the ocean that have a...Ch. 16 - How many times a minute does a boat bob up and...Ch. 16 - Scouts at a camp shake the rope bridge they have...Ch. 16 - What is the wavelength of the waves you create in...Ch. 16 - What is the wavelength of an earthquake that...Ch. 16 - Radio waves transmitted through empty space at the...Ch. 16 - Your ear is capable of differentiating sounds that...Ch. 16 - (a) Seismographs measure the arrival times of...Ch. 16 - A Girl Scout is taking a 10.00-km hike to earn a...Ch. 16 - A quality assurance engineer at a frying pan...Ch. 16 - A pulse can be described as a single wave...Ch. 16 - A transverse wave on a string is modeled with the...Ch. 16 - Consider the wave function...Ch. 16 - A pulse is defined as y(x,t)=e2.77( 2.00( x2.00m/s...Ch. 16 - A wave is modeled at time t=0.00s with a wave...Ch. 16 - A wave is modeled with the function...Ch. 16 - A surface ocean wave has an amplitude of 0.60 m...Ch. 16 - A wave is modeled by the wave function...Ch. 16 - A transverse wave on a string is described with...Ch. 16 - A swimmer in the ocean observes one day that the...Ch. 16 - Consider a wave described by the wave function...Ch. 16 - Consider two waves defined by the wave functions...Ch. 16 - Consider two waves defined by the wave functions...Ch. 16 - The speed of a transverse wave on a string is...Ch. 16 - Transverse waves are sent along a 5.00-m-long...Ch. 16 - A copper wire has a density of =8920 kg/m3, a...Ch. 16 - A piano wire has a linear mass density of =4.95103...Ch. 16 - A string with a linear mass density of =0.0060...Ch. 16 - A cord has a linear mass density of =0.0075 kg/m...Ch. 16 - A string is 3.00 m long with a mass of 5.00 g. The...Ch. 16 - Two strings are attached to poles, however the...Ch. 16 - Two strings are attached to poles, however the...Ch. 16 - Transverse waves travel through a string where the...Ch. 16 - Two strings are attached between two poles...Ch. 16 - Two strings are attached between two poles...Ch. 16 - The note E4 is played on a piano and has a...Ch. 16 - Two transverse waves travel through a taut string....Ch. 16 - A sinusoidal wave travels down a taut, horizontal...Ch. 16 - The speed of a transverse wave on a string is...Ch. 16 - A string of length 5 m and a mass of 90 g is held...Ch. 16 - Ultrasound of intensity 1.50102W/m2 is produced by...Ch. 16 - The low-frequency speaker of a stereo set has...Ch. 16 - To increase the intensity of a wave by a factor of...Ch. 16 - A device called an insolation meter is used to...Ch. 16 - Energy from the Sun arrives at the top of Earth’s...Ch. 16 - Suppose you have a device that extracts energy...Ch. 16 - A photovoltaic array of (solar cells) is 10.0%...Ch. 16 - A microphone receiving a pure sound tone feeds an...Ch. 16 - A string with a mass of 0.30 kg has a length of...Ch. 16 - The power versus time for a point on a string...Ch. 16 - A string is under tension FT1. Energy is...Ch. 16 - A 250-Hz tuning fork is struck and the intensity...Ch. 16 - A sound speaker is rated at a voltage of P=120.00...Ch. 16 - The energy of a ripple on a pond is proportional...Ch. 16 - Consider two sinusoidal waves traveling along a...Ch. 16 - Consider two sinusoidal sine waves traveling along...Ch. 16 - Consider two sinusoidal sine waves traveling along...Ch. 16 - Two sinusoidal waves are moving through a medium...Ch. 16 - Two sinusoidal waves are moving through a medium...Ch. 16 - Two sinusoidal waves are moving through a medium...Ch. 16 - Consider two waves y1(x,t) and y2(x,t) that are...Ch. 16 - Two sinusoidal waves, which are identical except...Ch. 16 - Two sinusoidal waves, which are identical except...Ch. 16 - Consider two wave functions,...Ch. 16 - Consider two wave functions,...Ch. 16 - Consider two wave functions that differ only by a...Ch. 16 - A wave traveling on a Slinky® that is stretched to...Ch. 16 - A 2-m long string is stretched between two...Ch. 16 - Consider the experimental setup shown below. The...Ch. 16 - A cable with a linear density of =0.2 kg/m is hung...Ch. 16 - Consider a rod of length L, mounted in the center...Ch. 16 - Consider two wave functions...Ch. 16 - A 2.40-m wire has a mass of 7.50 g and is under a...Ch. 16 - A string with a linear mass density of 0.0062 kg/m...Ch. 16 - A string with a linear mass density of 0.0075 kg/m...Ch. 16 - Two sinusoidal waves with identical wavelengths...Ch. 16 - A string, fixed on both ends, is 5.00 m long and...Ch. 16 - A string is fixed at both end. The mass of the...Ch. 16 - The frequencies of two successive modes of...Ch. 16 - A string is fixed at both ends to supports 3.50 m...Ch. 16 - Sine waves are sent down a 1.5-m-long string fixed...Ch. 16 - Ultrasound equipment used in the medical...Ch. 16 - Shown below is the plot of a wave function that...Ch. 16 - The speed of light in air is approximately...Ch. 16 - A radio station broadcasts radio waves at a...Ch. 16 - A sunbather stands waist deep in the ocean and...Ch. 16 - A tuning fork vibrates producing sound at a...Ch. 16 - A motorboat is traveling across a lake at a speed...Ch. 16 - Use the linear wave equation to show that the wave...Ch. 16 - Given the wave functions y1(x,t)=Asin(kxt) and...Ch. 16 - A transverse wave on a string is modeled with the...Ch. 16 - A sinusoidal wave travels down a taut, horizontal...Ch. 16 - A transverse wave on a string (=0.0030kg/m) is...Ch. 16 - A transverse wave on a horizontal string...Ch. 16 - A student holds an inexpensive sonic range finder...Ch. 16 - A wave on a string is driven by a string vibrator,...Ch. 16 - A traveling wave on a string is modeled by the...Ch. 16 - A transverse wave on a string has a wavelength of...Ch. 16 - (a) What is the intensity of a laser beam used to...Ch. 16 - Consider two periodic wave functions,...Ch. 16 - Consider two periodic wave functions,...Ch. 16 - A trough with dimensions 10.00 meters by 0.10...Ch. 16 - A seismograph records the S- and P-waves from an...Ch. 16 - Consider what is shown below. A 20.00-kg mass...Ch. 16 - Consider the superposition of three wave functions...Ch. 16 - A string has a mass of 150 g and a length of 3.4...Ch. 16 - A standing wave is produced on a string under a...Ch. 16 - A string with a length of 4 m is held under a...Ch. 16 - A copper wire has a radius of 200 µ m and a length...Ch. 16 - A pulse moving along the x axis can be modeled as...Ch. 16 - A string with a linear mass density of =0.0085...Ch. 16 - Consider two wave functions y1(x,t)=Asin(kxt) and...Ch. 16 - The wave function that models a standing wave is...Ch. 16 - Consider two wave functions y1(x,t)=Asin(kxt) and...
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