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- University physics volume 1
- Unit 2. waves and acoustics
- Waves
- Interference of waves
A long, tight spring is held by two students, one student holding each end. Each student gives the end a flip sending one wavelength of a sinusoidal wave down the spring in opposite directions. When the waves meet in the middle, what does the wave look like?
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Many of the topics discussed in this chapter are useful beyond the topics of mechanical waves. It is hard to conceive of a mechanical wave with sharp corners, but you could encounter such a wave form in your digital electronics class, as shown below. This could be a signal from a device known as an analog to digital converter, in which a continuous voltage signal is converted into a discrete signal or a digital recording of sound. What is the result of the superposition of the two signals?
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A string of a constant linear mass density is held taut by two students, each holding one end. The tension in the string is constant. The students each send waves down the string by wiggling the string. (a) Is it possible for the waves to have different wave speeds? (b) Is it possible for the waves to have different frequencies? (c) Is it possible for the waves to have different wavelengths?
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Problems
Consider two sinusoidal waves traveling along a string, modeled as
and
What is the height of the resultant wave formed by the interference of the two waves at the position
at time
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Consider two sinusoidal sine waves traveling along a string, modeled as
and
What is the height of the resultant wave formed by the interference of the two waves at the position
at time
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Consider two sinusoidal sine waves traveling along a string, modeled as
and
What is the wave function of the resulting wave? [
Hint: Use the trig identity
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Two sinusoidal waves are moving through a medium in the same direction, both having amplitudes of 3.00 cm, a wavelength of 5.20 m, and a period of 6.52 s, but one has a phase shift of an angle
. What is the phase shift if the resultant wave has an amplitude of 5.00 cm? [
Hint: Use the trig identity
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Two sinusoidal waves are moving through a medium in the positive
x -direction, both having amplitudes of 6.00 cm, a wavelength of 4.3 m, and a period of 6.00 s, but one has a phase shift of an angle
What is the height of the resultant wave at a time
and a position
?
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Two sinusoidal waves are moving through a medium in the positive
x -direction, both having amplitudes of 7.00 cm, a wave number of
an angular frequency of
and a period of 6.00 s, but one has a phase shift of an angle
What is the height of the resultant wave at a time
and a position
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Consider two waves
and
that are identical except for a phase shift propagating in the same medium. (a)What is the phase shift, in radians, if the amplitude of the resulting wave is 1.75 times the amplitude of the individual waves? (b) What is the phase shift in degrees? (c) What is the phase shift as a percentage of the individual wavelength?
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Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is
What are the angular frequency, wave number, amplitude, and phase shift of the individual waves?
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Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is
What are the period, wavelength, amplitude, and phase shift of the individual waves?
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Consider two wave functions,
and
(a) Using a spreadsheet, plot the two wave functions and the wave that results from the superposition of the two wave functions as a function of position
for the time
(b) What are the wavelength and amplitude of the two original waves? (c) What are the wavelength and amplitude of the resulting wave?
a.
;
b.
; c.
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Consider two wave functions,
and
(a) Verify that
is the solution for the wave that results from a superposition of the two waves. Make a column for
x ,
,
,
, and
Plot four waves as a function of position where the range of
x is from 0 to 12 m.
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Consider two wave functions that differ only by a phase shift,
and
Use the trigonometric identities
and
to find a wave equation for the wave resulting from the superposition of the two waves. Does the resulting wave function come as a surprise to you?
The result is not surprising because
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Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
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Source:
OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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