A pulse (gas) travelling along a fine straight uniform tube filled with gas causes the density at any time t and distance x from the origin where the velocity is u_0 to become ?_0ϕ(vt-x). Prove that the velocity u (at time t and distance x from the origin) is given by

A pulse (gas) travelling along a fine straight uniform tube filled with gas causes the density at any time t and distance x from the origin where the velocity is u_0 to become ?_0ϕ(vt-x). Prove that the velocity u (at time t and distance x from the origin) is given by

Related questions

Q: A high-speed aircraft takes-off in the xyz-plane and the coordinates are given by x(t) = αt, y(t) =…

Q: Given the curve C parametrized by the vector equation r (t)=3sin(t)i+[2−sin(t)+cos(t)]j−3cos(t)k,…

A: The vector equation is : r (t)=3sin(t)i^+[2−sin(t)+cos(t)]j^−3cos(t)k^, t∈[0;2π] The tangent…

Q: Problem 6: During service, a tennis ball is struck at height h = 1.8 m above a tennis court and…

Q: Consider a point particle with position vector r = (x, y, z) in Cartesian coordinates, moving with a…

A: The objective of the question is to understand the motion of a particle in three dimensions, given…

Q: (a) Substitute for r as a function of time, and derive the complete equation of motion for 0. (b)…

A: Since, no specific subpart was mentioned, so I have answered the first three subpart. If you want…

Q: Part (a) What is the magnitude of the impulse I, in kilogram meters per second, the golf ball…

A: Given : Mass of the ball, m = 0.1045 kg Initial height, h1 = 3.35 m Height reached after bouncing,…

Q: Part (b) How long, tfin seconds, does the tennis ball move before striking the court? ケ=

A: The tennis ball is struct at a vertical height of 1.95 m above the ground of the tennis court. After…

Q: Find a formula for the average velocity, vav(t), on the time interval [t, 7] for t n. Vav (t) Find…

A: An object moving in a straight line with a displacement function s(t), then its avg velocity between…

Q: A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on…

A: We will first write relations connecting cartesian and spherical coordinates. Using these, we…

Q: A particle, starting from position (2, 3, 4) was moved at a constant rate in a three-dimensional…

Q: (a) As the milk fills the bowl, the milk level reaches a point where the diameter of the bowl is d1…

Q: motion of the point K moving along the plane is given by the equation x = 3sin (t), y = 2cos (t).…

A: GIVEN x= 3 sint y=2 sint

Q: show that the function y(x)=Ax^n (A and n are constants) will give a straight line on a log-log…

A: The provided function is expressed as y=Axn

Q: Find a(t) and (a(t)) for motion around a circle of radius R with constant speed v.

A: Given, Radius r =R velocity v =v

Q: Let vectors A⃗=(2,−4) A → = ( 2 , − 4 ) and B⃗=(−3,1) B → = ( − 3 , 1 ) . Calculate the following:…

Q: Let z = z(t) and y = y(t) (where tis the variable of time) be the horizontal and vertical positions…

A: Given: Position in XY plane as X=xtY=yt At point α,β, where α<0β>0 means particle is in…

Q: EXAMPLE 1.19 Supp of 6.625 x 1034 Js. E thrown with eneed

A: Given:- the mass m= 66.25 gm = 66.25 x 10 -3 kg h = 6.625 x 10-3 Js The thrown speed v = 5 m/s…

Q: (e) Finally we return to eqs.(2.101)-(2.103) in Griffiths. Show that if W(4. 0) = . 1 Y(x,0) dk o(k)…

A: Concept used: Fourier transform is used to move from position space (x-space) to momentum space…

Q: Find the total mass of an L-shaped rod consisting of the segments(2t, 2) and (2, 2 − 2t) for 0 ≤ t ≤…

A: Given data: Segments of rod, 2t,2; 2,2-2t for 0≤t≤1 Mass density, ρx,y=x2y g/cm

Q: derive ω = αt + ω0

A: Sorry for the inconvenience. As you have posted multiple questions in one question, so as per…

Q: derive θ = θ0 + (ω + ω0) t/2.

A: To derive- θ=θo+(ω+ωo)t2 USING above two results Mic test…

Q: Salt water with a density of 6 = 0.25 g/ cm flows over the curve r(t) = /5ti+ 2ij. Osts5, according…

A: Given: ς= 0.25 g/cm2 rt=5ti+2tj

Q: How would you approach solving for change in x?

A: 1.Step 1It is given that

Q: A particle P moves along the line x+y=2 in the z plane with a uniform speed 3√2 ft /sec from the…

Q: The following data for the instantaneous velocity, v, versus time, t, was obtained to fit he…

A: The given set of data is: Time (t) Velocity (v) 0.2 0.332 0.4 0.508 0.6 0.645 0.8 0.798…

Q: Evaluate the integral from -∞ to ∞ of the expression exp ip²t 2mħ 4ah² + ipad + fact that the…

Q: In problem OP2.40, you were working with a movie director and investigated a cowboy sliding off a…

Q: Consider the 2-sphere with the metric dr² 1-p² (1) ds² = gabdxdxb =a² +r²d0² where a is a constant…

Q: If ů = (i) × (j) and i = (j) x (-k), find the length and direction of ủ ×ỉ and i x ủ. Length of u x…

Q: Your character starts at position po with initial velocity Each frame, it moves with constant…

A: We have 3 equations of motion to describe motion for constant acceleration. The displacement is…

Q: a certain corner of a room is selected as the origin of a retangualr coordinate system. A fly is…

A: Write the given values with suitable variables. x=3.7y=1.3

Q: Show that the acceleration of any object down an incline where friction behaves simply (that is,…

Q: A cubic pool with edges of length L is filled with water described by the flow vector J below: J(x,…

A: Given data: Flow vector J is, J→x,y,z=-2J0txyi^+yzj^+xzk^

Q: Sketch or computer plot a graph of the function y = e−x2.

A: The given function; y=e-x2

Question

A pulse (gas) travelling along a fine straight
uniform tube filled with gas causes the density
at any time t and distance x from the origin
where the velocity is u_0 to become ?_0ϕ(vt-x).
Prove that the velocity u (at time t and distance
x from the origin) is given by