determine the amplitude and phase of the resulting wave
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This problem involves adding two waves with the same angular frequency. Please calculate the sum of the two waves ? = ?1+?2 given below and determine the amplitude and phase of the resulting wave (as a function of A1 and A2). A graphic or algebraic solution is acceptable:
A) ?1(r,t) = A1ei(-ωt) ?2(r,t) = A2ei((π/2)-ωt)
B) ?1(r,t) = A1ei(-ωt) ?2(r,t) = A2ei(π-ωt)
C) ?1(r,t) = A1ei(-ωt) ?2(r,t) = A2ei((3π/2)-ωt)
D) ?1(r,t) = A1ei(-ωt) ?2(r,t) = A2ei((2π)-ωt)
E) ?1(r,t) = A1ei(-ωt) ?2(r,t) = A2ei((π/3)-ωt)
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- Consider two sinusoidal waves: fi = A1 cos (kz – wt + ø1) and f2 = A2 cos (kz – wt + 02). We can write their complex forms as fi =Aje(kz-wt+61) = áeï(kz-wt) f2 =Aze(kz-wt+62) = Ãze³(kz-wt) where the complex amplitudes Ã1 = Ajeø1 and Ã, = Azeió2 Now suppose we want to combine the two: fs = fi + f2 = Ãze(k3:-w3t) = Azeiøs ei(kzz=wzt) Find expressions for A3, $3, k3, and w3.The equation for the displacement of a stationary wave on a string is given by y = 2 (sin 5πt)(cos 6πx), where x and y are in meters, and t is in seconds. Determine: b. the amplitude of the point P which lies at a distance of 75 cm from the end of the reflection!2π.χ. λι -₁), 1. In the geometry of the following figure, the wave in region 1 is given by y₁(x)=C₁sin (5 where ₁ = 4.97 cm, and ₁ = -65.3°. In region 2, the wavelength is ₂ = 10.5 cm. The boundary A is located at x = 0, and the boundary B is located at x = L, where L = 20.0 cm. Find the wave functions in regions 2 and 3. [2] Incident A B Transmitted wave wave и Reflected wave Glass Air (region 1) (region 2) Air (region 3) (a)
- D, mm 1 0 00000000 The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is O 1.0 mm. O zero. O 1.8 mm. O 1.4 mm. O 2.0 mm.a° y(z,t) 1 d*y(x,t) Which of the following wave functions satisfies the wave equation? A.) y(x, t) = A cos(kæ + wt) B.) y(x, t) = A sin(kx +wt) C.) y(x, t) = A[cos(kæ) + cos(wt)] For any of the equations above that satisfy the wave equation what are the transverse velocity and acceleration of a particle at point x?Two progressive waves ?1(?,?)=?sin(2???−??)y1(x,t)=Asin(2πλx−ωt) and ?2(?,?)=?sin(2???−??−?2)y2(x,t)=Asin(2πλx−ωt−π2) travel in the same direction. Calculate the speed of the wave produced as a result of interference of these two waves. Take ?=5A=5 cm, ?=4λ=4 m and ?=31.4ω=31.4 Hz. Provide your answer in SI units.
- AW-1 A standing wave on a string is produced by two waves which travel along the string in opposite directions. The displacements of the two component waves are given by the functions shown below, where all quantities are in SI units. D₁(x, t) = (0.10)sin(4.0x – 9.5t) and D₂(x, t) = (0.10)sin(4.0x + 9.5t) a) Find the function that describes the overall standing wave. This will be the total displacement of the two component waves, D₁(x, t) = D₁(x,t)+D₂(x,t) b) What is the amplitude of the standing wave, in meters? c) What is the wavelength of the standing wave, in meters? d) What is the frequency of the standing wave, in Hz? What is the speed of each component wave, in m/s?please answer parts c, d, and e