(II) The displacement of a bell-shaped wave pulse is described by a relation that involves the exponential function: D ( x , t ) = A e − α ( x − v t ) 2 where the constants A = 10.0 m, α = 2.0 m –2 , and v = 3.0 m/s. ( a ) Over the range –10.0 m ≤ x ≤ + 10.0 m, use a graphing calculator or computer program to plot D ( x , t ) at each of the three times t = 0, t = 1.0, and t = 2.0 s. Do these three plots demonstrate the wave-pulse shape shifting along the x axis by the expected amount over the span of each 1.0-s interval? ( b ) Repeal part ( a ) but assume D ( x , t ) = A e − α ( x + v t ) 2 .
(II) The displacement of a bell-shaped wave pulse is described by a relation that involves the exponential function: D ( x , t ) = A e − α ( x − v t ) 2 where the constants A = 10.0 m, α = 2.0 m –2 , and v = 3.0 m/s. ( a ) Over the range –10.0 m ≤ x ≤ + 10.0 m, use a graphing calculator or computer program to plot D ( x , t ) at each of the three times t = 0, t = 1.0, and t = 2.0 s. Do these three plots demonstrate the wave-pulse shape shifting along the x axis by the expected amount over the span of each 1.0-s interval? ( b ) Repeal part ( a ) but assume D ( x , t ) = A e − α ( x + v t ) 2 .
(II) The displacement of a bell-shaped wave pulse is described by a relation that involves the exponential function:
D
(
x
,
t
)
=
A
e
−
α
(
x
−
v
t
)
2
where the constants A = 10.0 m, α = 2.0 m–2, and v = 3.0 m/s. (a) Over the range –10.0 m ≤ x ≤ + 10.0 m, use a graphing calculator or computer program to plot D(x, t) at each of the three times t = 0, t = 1.0, and t = 2.0 s. Do these three plots demonstrate the wave-pulse shape shifting along the x axis by the expected amount over the span of each 1.0-s interval? (b) Repeal part (a) but assume
D
(
x
,
t
)
=
A
e
−
α
(
x
+
v
t
)
2
.
A creature can detect very small objects, such as an insect whose length is approximately equal to one wavelength of the sound the bat makes. If a bat emits chirps at a frequency of 56 kHz, and if the speed of sound in air is 315 m/s,
what is the smallest insect (in mm) the bat can detect?
A Moving to another question will save this response
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(d) x(t) = sin(3pi t) (third harmonic sine) and h(t) = sin (4pi t) (fourth harmonic sine)
Answer d only
4:29 O M
In an oscillatory motion of a simple
pendulum, the ratio of the maximum
angular acceleration, O"max, to the
maximum angular velocity, O'max, is t
s^(-1). What is the time needed for the
pendulum to complete two oscillations?
1 sec
0.5 sec
0.25 sec
4 sec
2 sec
The wavefunction of a mechanical wave on
a string is described by: y(x,t) =
0.012cos(TtX-100rtt-2Tt/3), where x and y
are in meters and t is in seconds. The
transverse velocity of an element on the
string at the left end (x = 0), at time t = 0 is:
-0.6V3n m/s
-0.6π m/s
+0.6n m/s
+0.6v3n m/s
None of the listed
II
O O
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