Now we know that intensity varies directly with the square of the amplitude of the waves Squaring and adding the above two equations we getĪ = √( b 2 + 2ab Cos θ + a 2 ) -–iv) Therefore comparing the coefficients of Sin ωt and Cos ωt on both sides If the resultant amplitude is considered as A then y = A sin (θ + ωt) = b sin (θ + ωt) + a sin ωt. Applying the principle of superposition stated earlier we get y = b sin (θ + ωt) + a sin ωt. Here b and a are the amplitude of the waves and θ is the difference in phase between the two waves which is constant. Displacement of each separate wave is given by y 2 = b sin ( θ + ωt ) and y 1 = a sin ωt. The difference only occurs in the phases. The two waves are at the specific point P at the given time. Then the displacement of the resultant wave is given as y = y 2 + y 1. Suppose two waves having a vertical displacement y 2 and y 1 superimpose at a particular point of p. Resultant intensity in interference of two waves The effect of disruption of the two waves will lead to the medium taking a new shape that will ultimately result in the combined effect of the two waves. In this context, the aspect of wave disturbance is important which is defined as a specific condition in which two specific waves hit or meet each other while moving in the same direction. The amplitude and intensity of these resultant waves can be the same, lesser, or greater than the original interfering waves. The interference of two waves is said to be the phenomenon in which two waves overlap to form a resultant wave. On overlapping of these two waves, the resultant displacement is obtained. Then the displacement of the elements within the two waves can be represented as y 2 (x, t) and y 1 (x, t).
Let two waves be considered to be traveling simultaneously concerning the same string. The string oscillates with the same frequency as the string vibrator, from which we can find the angular frequency.The superposition principle of the waves states that the resulting displacement of several waves within a medium at a given point can be regarded as the vector sum of the displacement of each wave produced by each particular wave at that point. The speed of the wave on the string can be derived from the linear mass density and the tension. It should be noted that although the rate of energy transport is proportional to both the square of the amplitude and square of the frequency in mechanical waves, the rate of energy transfer in electromagnetic waves is proportional to the square of the amplitude, but independent of the frequency. If two mechanical waves have equal amplitudes, but one wave has a frequency equal to twice the frequency of the other, the higher-frequency wave will have a rate of energy transfer a factor of four times as great as the rate of energy transfer of the lower-frequency wave. We will see that the average rate of energy transfer in mechanical waves is proportional to both the square of the amplitude and the square of the frequency.
If the energy of each wavelength is considered to be a discrete packet of energy, a high-frequency wave will deliver more of these packets per unit time than a low-frequency wave.
The energy of the wave depends on both the amplitude and the frequency.
The larger the amplitude, the higher the seagull is lifted by the wave and the larger the change in potential energy. Work is done on the seagull by the wave as the seagull is moved up, changing its potential energy. Consider the example of the seagull and the water wave earlier in the chapter ( Figure). Large ocean breakers churn up the shore more than small ones. Loud sounds have high-pressure amplitudes and come from larger-amplitude source vibrations than soft sounds. Large-amplitude earthquakes produce large ground displacements. The amount of energy in a wave is related to its amplitude and its frequency.
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