Question
In: Physics
A particular wave pulse is described by the function f(x,t) = (2/??) exp[-(x + ct)²]. Explain...
A particular wave pulse is described by the function f(x,t) = (2/??) exp[-(x + ct)²]. Explain how to determine the velocity of the pulse and why that works. In particular, explain why the sign of c determines the direction of propagation. (In case you aren’t familiar, “expo” means “exponential” and exp(x) is often used instead of e? when the argument gets too big to fit comfortably as an exponent. Not that this question requires knowing any of this.)
Solutions
genius_generous answered 2 years agoRelated Solutions
1.)is the function f (x) = x exp^ (-x ^ 2/2) a proper function of the...
1.)is the function f (x) = x exp^ (-x ^ 2/2) a proper
function of the operator O= d2 / dx2-x2? if so, what is the
intrinsic value?
2.)is the function f (x) = exp^ (4ix) -exp ^(-4ix) its own function
of the operator d2 / dx2? if so, what is the intrinsic value?
3.)is the function f (x) = exp^ (2ix) -exp ^(-2ix) a proper
function of the operator d^2 / dx^2? if so, what is the intrinsic
value?...
Find the derivative of the function f(t)=arccsc〖(-t^2)〗 f(x)=arccot√x y=ln〖t^2 〗-arctan〖t/2〗 f(x)=arcsecx+arccscx...
Find the derivative of the function
f(t)=arccsc〖(-t^2)〗
f(x)=arccot√x
y=ln〖t^2 〗-arctan〖t/2〗
f(x)=arcsecx+arccscx
y=arctan〖x/2〗+1/(2(x^2+4))
Use implicit differentiation to find an equation of
the tangent line the graph of the equation at the given
point.
arctan(x+y)=y^2+π/4, (1,0)
a) For the function f (x) = x – exp(−x2), do a calculation by hand using...
a) For the function f (x) = x – exp(−x2), do a calculation by
hand using a calculator to find the root to an accuracy of 0.1. At
most, five iterations (or fewer) are needed to obtain the desired
accuracy.
b) For f (x) = x2 – sin x, x0 = 1⁄2, do three iterations of
Newton’s method (by hand); tabulate the result.
A traveling wave along the x-axis is given by the following wave function ψ(x, t) =...
A traveling wave along the x-axis is given by the following wave
function ψ(x, t) = 4.5 cos(2.1x - 11.8t + 0.52),where x in meter, t
in seconds, and ψ in meters. Find
a) the frequency, in hertz
b)The wavelength in meters.
c) The wave speed, in meters per second.
d) The phase constant in radians.
The wave function for a harmonic wave on a string is y(x, t) = (0.0010 m)...
The wave function for a harmonic wave on a string is
y(x, t) = (0.0010 m) sin((69.8
m-1)x + (309 s-1)t).
(a) In what direction does this wave travel?
+x-x
What is its speed?
m/s
(b) Find the wavelength of this wave.
m
Find its frequency.
Hz
Find its period.
s
(c) What is the maximum speed of any string segment?
m/s
A wave in a string has a wave function given by: y (x, t) = (0.0300m)...
A wave in a string has a wave function given by: y (x, t) =
(0.0300m) sin [(5.35 m^-1) x + (1.63 s^-1) t]
where t is expressed in seconds and x in meters.
Determine:
a) the amplitude of the wave
b) the frequency of the wave
c) wavelength of the wave
d) the speed of the wave
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) =
b(a2 - x2) for -a ≤ x ≤ a and ψ(x)=0 for x ≤
-a and x ≥ a, where a and b are positive real
constants.
(a) Using the normalization condition, find b in terms of
a.
(b) What is the probability to find the particle at x =
0.21a in a small interval of width 0.01a?
(c) What is the probability for the particle to be found between x...
A particle is described by the wave function ψ(x) = b(a2 - x2) for -a ≤...
A particle is described by the wave function ψ(x) = b(a2 - x2)
for -a ≤ x ≤ a and ψ(x)=0 for x ≤ -a and x ≥ a , where a and b are
positive real constants.
(a) Using the normalization condition, find b in terms of a.
(b) What is the probability to find the particle at x = 0.33a in
a small interval of width 0.01a?
(c) What is the probability for the particle to be found...
Find the domain for each function please explain. f(x)=10x^2 + x f(x)= -2/x^2
Find the domain for each function please explain. f(x)=10x^2 + x
f(x)= -2/x^2
If the moment-generating function of X is M(t) = exp(3 t + 12.5 t2) = e3...
If the moment-generating function of X is M(t) = exp(3 t + 12.5
t2) = e3 t + 12.5 t2.
a. Find the mean and the standard deviation of
X.
Mean =
standard deviation =
b. Find P(4 < X < 16). Round your answer
to 3 decimal places.
c. Find P(4 < X2 < 16). Round
your answer to 3 decimal places.
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