PD-2 Consider three different waves, each with amplitude A, which meet at the same point in space at the same moment in time. The phase difference between successive waves is 60°. (a) Construct a phasor diagram showing the addition of these waves. (b) What is the amplitude of the resultant wave (in terms of A)? (c) What is the phase difference between the first wave in the phasor diagram and the resultant wave?

Consider 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.

Consider two periodic wave functions, y1 (x, t) = A sin (kx − ωt) and y2 (x, t) = A sin (kx − ωt + ϕ). (a) For what values of ϕ will the wave that results from a superposition of the wave functions have an amplitude of 2A? (b) For what values of ϕ will the wave that results from a superposition of the wave functions have an amplitude of zero?

An interface is formed between a block of aluminium (with an acoustic impedance of 1.8 x 107 kg m2 s') and a block of copper (with an acoustic impedance of 4.6 x 107 kg m-2 s-1). Longitudinal sound waves travelling through the aluminium are normally incident on the boundary, and are partially reflected. a) What is the ratio of the amplitude of the reflected wave to that of the incident wave? Number b) What is the ratio of the amplitude of the transmitted wave to that of the incident wave? Number c) What percentage of the incident power is transmitted? Number d) What percentage of the incident power is reflected? Number % Ouit P Sove Questi

For a certain transverse wave, the distance between two successive crests is 1.77 m. And starting from the time when a crest passes through a certain point, 5 subsequent crests will then pass the same point over a time of 10.3 s. Calculate the wave speed (in unit of ms-1).

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?

Two wave pulses, each of wavelength λ, are traveling toward each other along a rope as shown. When both pulses are in the region between points X and Y, which are a distance λ apart, the shape of the rope is X Y Ã -Y A

To further explore what this equation means, consider four sets of identical waves that move in the +x direction. A photo is taken of each wave at time t and is displayed in the figures below. Rank these sets of waves on the basis of the maximum amplitude of the wave that results from the interference of the two waves in each set. Rank from largest amplitude on the left to smallest amplitude on the right. To rank items as equivalent, overlap them. Reset Help Wane Wane Wane 20 Wane 2 Wave Wave O The correct ranking cannot be determined.