Question

In: Physics

When two waves are overlapped on each other in the same medium, are they still two...

When two waves are overlapped on each other in the same medium, are they still two waves, or is the result a single wave? explain

Solutions

Expert Solution

Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium.

To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. Let's suppose that each displaced upward 1 unit at its crest and has the shape of a sine wave. As the sine pulses move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be an upward displaced sine pulse with an amplitude of 2 units.

The task of determining the shape of the resultant demands that the principle of superposition is applied. The principle of superposition is sometimes stated as follows:

When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.


Related Solutions

When two waves in the same medium hit each other, the resulting displacement of the medium...
When two waves in the same medium hit each other, the resulting displacement of the medium is A. Either larger or smaller than the displacement of either wave acting alone, depending on the signs of the displacements of the two waves. B. Always smaller than the displacement due to either wave acting alone. C. Always larger than the displacement due to either wave acting alone.
If two sinusoidal waves with amplitudes 4A and 8A are in phase with each other, their...
If two sinusoidal waves with amplitudes 4A and 8A are in phase with each other, their resulting amplitude will be 10A. True or False?
1. There are two players. Each names an amount at the same time as the other....
1. There are two players. Each names an amount at the same time as the other. They can say $0 or say $10 or anything in between, even fractions of cents. If the amounts total $10 or less they get what they named. If they total more than $10 they get $0. What are the Nash equilbria? To solve this try some pairs of amounts. If they aren’t equilibria – if one player or both could do better by changing...
The wave functions of two waves traveling in the same direction are given below. The two...
The wave functions of two waves traveling in the same direction are given below. The two waves have the same frequency, wavelength, and amplitude, but they differ in their phase constant. y1 (x,t) = 2 sin⁡(2πx ‒ 20πt), and y2 (x,t) = 2 sin(2πx ‒ 20πt + φ), where, y is in centimetres, x is in meters, and t is in seconds. Assume that the two waves start to propagate at the same instant, t_0,1 = t_0,2 = 0 sec,...
Two sinusoidal waves combining in a medium are described by the following wave functions, where x...
Two sinusoidal waves combining in a medium are described by the following wave functions, where x is in centimeters and t is in seconds. y1 = (1.0 cm) sin π(x + 0.20t) y2 = (1.0 cm) sin π(x - 0.20t) Determine the maximum transverse position of an element of the medium at the following positions. (a) x = 0.270 cm cm (b) x = 0.400 cm cm (c) x = 1.80 cm cm (d) Find the three smallest values of...
Two speakers spaced emitting identical sound waves in phase with each other of wavelength 1.00 m...
Two speakers spaced emitting identical sound waves in phase with each other of wavelength 1.00 m are spaceced 5.00 m from eachother. At what minimal distance (in m) from one of them should an observer stand to hear almost nothing (the first minimum)(__________)? The first maximum after this minimum (__________)? Second minimum (__________)? Second maximum (__________)? Third minimum (__________)? Third maximum (__________)? How many minima overall can be observed (__________)? How many maxima (__________)?
Two cars are on a level air track. They have the same mass as each other....
Two cars are on a level air track. They have the same mass as each other. The red car is given a push so that it moves toward the blue car with an initial speed of 2 m/s, while the blue car is given a push so that it moves toward the red car with an initial speed of 4 m/s. If the cars completely stick together, find their combined speed after the collision. 2. This is an inelastic collision,...
Q.2.Two sinusoidal waves combining in a medium are described by the wave functions y1 = (0.3m...
Q.2.Two sinusoidal waves combining in a medium are described by the wave functions y1 = (0.3m ) cos (2πx +40πt) y2=( 0.3 m) sin (2πx +40πt ) (i). What will be the resultant displacement wave function expression and what type of the resultant wave will be generated by it. [3] (ii). What will be the amplitude, frequency and the speed of the resultant wave? [3] (iii).Find the transverse velocity and transverse acceleration at x= 0.25m, and t= 2sec?
Two speakers spaced a distance 1.5 m apart emit coherent sound waves at a frequency of 680 Hz in all directions. The waves start out in phase with each other.
Two speakers spaced a distance 1.5 m apart emit coherent sound waves at a frequency of 680 Hz in all directions. The waves start out in phase with each other. A listener walks in a circle of radius greater than 1 m centered on the midpoint of the two speakers. At how many points does the listener observe destructive interference? The listener and the speakers are all in the same horizontal plane and the speed of sound is 340 m/s....
Two truckers are traveling directly away from each other at the same speed. If one trucker...
Two truckers are traveling directly away from each other at the same speed. If one trucker sounds her horn at a frequency of 236 Hz, and the other trucker hears a frequency of 223 Hz, determine the speed of the trucks. Use the speed of sound as 343 m/s.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT