2Brt y(x, t) = eA² e A e -B²t2
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We can say that the equation of the image considering that A = 7 m and B = 7 s-1, can it represent a propagating wave? If so, what is its direction and velocity? Consider the x axis horizontal and increasing to the right.
Choose the correct alternative:
a) No.
b) Yes. Right and v = 49 m/s.
c) Yes. Left and v = 49 m/s.
d) Yes. Right and v = 98 m/s.
e) Yes. Left and v = 98 m/s.
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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 w3.3.7 Two sinusoidal waves in a string are defined by the wave functions Y₁ = 2.20 sin (17.0x - 35.0t) Y₂ = 2.20 sin (29.0x - 45.0t) where x, y₁, and y₂ are in centimeters and it is in seconds. (a) What is the phase difference between these two waves at the point x = 5.00 cm at t = 2.00 s? (Your answer should be between 0° and 360°.) (b) What is the positive x value closest to the origin for which the two phases differ by ± at t = 2.00 s? (At that location, the two waves add to zero.) cmConsider a monochromatic green lightwave with wavelength λ = 550 nm (1 nm = 1 * 10-9m). Assuming the speed of light in vacuum (which is close to the one in air) to be c = 3 * 108m/s, then: A. Calculate the period τ and the optical frequency v for green light? B. Write a sinusoidal harmonic wave with unit amplitude propagating towards the negative x-axis. Consider that for x = 0 and t = 0, the (initial) phase is (π/2). C. Plot the wave profile against x for following times: t = 0, 0.25τ, 0.5τ, and 0.75τ. Assume an arbitrary unit for the y-axis.
- 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.0.0058 kg/m is fixed at both ends. A 5.0-kg mass is hung from A string with a linear mass density of the string, as shown. If a pulse is sent along section A, what is the wave speed in section A and the wave speed in section B? %D B. A FA 35° 5 kg Image Description VA m/s VB = m/s B.X/10. It is √gd, so A water wave is a shallow-water wave if the water depth d is less than shown in hydrodynamics that the speed of a shallow-water wave is v = waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 100 m, are shallow-water waves when the water depth is less than 10 m. Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of 5.4 m at a distance of 100 m. Part A How long does it take a wave to move the last 100 m to the shore? Assume that the waves are so small that they don't break before reaching the shore. Express your answer to two significant figures and include the appropriate units. At = Value Units ?
- Show your complete solutions. Thank you.QUESTION 5 A transverse wave completes 12 full oscillations in two seconds. The wave moves at 31.2 m/s. Find the distance between two adjacent crests on the wave (in m). QUESTION 6 The linear density of a guitar string is 8.0 x 104 kg/m. A wave on the string has a frequency of 400 Hz and a wavelength of 60 cm. What is the tension in the string? QUESTION 7 The mathematical expression of a wave is given by y = 4.2 m Sin ( 1.2 rad/m x – 9.6 rad/s t). What is the speed of the wave (in m/s)? QUESTION 8 What is the sound intensity (in µW/m2) at 1.86 m from a 4 mW loudspeaker emitting sound uniformly in all directions?