Question: Prove that (x, t) = A cos (kx - t - /2) is equivalent to (x, t) = A sin (kx - t)

Prove that
ψ(x, t) = A cos (kx - ωt - π/2)
is equivalent to
ψ(x, t) = A sin (kx - ωt)

Step by Step Solution

★★★★★

3.40 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

yx t A coskx ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Optics Questions!

Q:

(a) Given that the position of an object is x(t) = A cos (t, show that vx(t) = (A sin (t. [Draw the velocity vector for point P in Fig. 10.17b and then find its x - component.] (b) Verify that the...

Q:

Time-Dependent Wave Function for a Free Particle One example of a time-dependent wave function is that of a free particle [one for which U(x) = 0 for all x] of energy E and x-component of momentum p....

Q:

Which of the following wave functions satisfies the wave equation? (a)y(x, I) = A cos (kx + wt); (b)y(x, I) =A sin (kx + w,); (c) y (x, t) = A(cos kx + cos wt). (d) For the wave of part(b), write the...

Q:

Please prove the following trig identities. i rig Identities Practice Day 5 Prove the following identities 1. (cos x - sin x) 2 = 1 - 2 sin x cos x 2. cos x sin x+ cos 3x - = cotx sin x 1 1 1 + =...

Q:

onometric Identities Prove the given identity. sec x csc x- sin x sec x= cos x csc x This quiz: 25 poi

Q:

a. D= (x ER|-85x4 - 2x2 - 3? a. (x - 1)(x + 1)(x -3) C. (x + 1)(x2 - 3) b. (x - 1) (x + 3) none of the above 7. Based on the graph of f(x) = x4 - 2x' + 3x + 2 shown, what are the real roots of x4 -...

Q:

pter 4 Quiz Name: alculus Date Period: Quotient Properties Pythagorean Properties tan x = Sin x _COSX sin x + cos x = 1 coS X cotx = - sin x tan x + 1 = secz x 1 + cot2 x = csc2 x For problems 1 - 6,...

Q:

please assist me with all of question 4 thank you very much 4. Prove the following identities. a) sin x(1+ cot x) =1 b) 1- cos x -tankcosxsinx 1 - cos x = sin x sin x cos.x sin x + -1 C) sin x d) tan...

Q:

Surface Plasmons consider a semi-infinite plasma on the positive side of the plane z = 0. A solution of Laplace's equation 2 = 0 in the plasma is i (x, z) = A cos kx e kz whence E si = kA cos kx...

Q:

If f: R R belongs to C(R) and f(j) is periodic for all j > 0, prove that Sf is term-by-term differentiable on R. In fact, show that uniformly for all j N. di f dxi (x) =-dx) (ak(f) cos kx + bk(f) sin...

Q:

Irrigation Supply is negotiating with a major hardware chain to supply heavy-duty sprinkler heads at $18,000 each year for 6 years. Irrigation Supply would need to retool at a cost of $20,000 to fill...

Q:

When Chinas clothing industry expands, the increase in world supply lowers the world price of clothing. a. Draw an appropriate diagram to analyze how this change in price affects consumer surplus,...

Q:

Admitting students to college. A selective college would like to have an entering class of 950 students. Because not all students who are offered admission accept, the college admits more than 950...

Q:

How characteristics of an industrial product influence international marketing activities

Q:

A 500-mL sealed flask contains nitrogen at a pressure of 76.00 cmHg. A tiny glass tube lies at the bottom of the flask. Its volume is 0.50 mL and it contains hydrogen gas at a pressure of 4.5 atm....

Q:

As shown in Fig. 16-2, two flasks are connected by an initially closed stopcock. One flask contains krypton gas at 500 mmHg, while the other contains helium at 950 mmHg. The stopcock is now opened so...

Q:

One method for estimating the temperature at the center of the Sun is based on the Ideal Gas Law. If the center is assumed to consist of gases whose average M is 0.70 kg/kmol, and if the density and...

Q:

Apple Inc., a U.S. based corporation, wants to purchase Technology Inc. a company based in Singapore. The current U.S. Treasury bond rate (Rus) is 4%. The expected inflation rate in the United States...

Q:

Kamal Fatehl production manager of Kennesaw Manufacturing, finds his profit at $28,000 inadequate for expanding his business. The bank is insisting on an improved profit picture prior to approval of...

Q:

What is true regarding P values? Group of answer choices, choose one. The definition of p-value begins with assuming a null hypothesis is false. The null hypothesis is usually the same as the...