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Beats; Resonance Interference Anytime Two Waves of the Same Type

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Beats; Resonance Interference Anytime Two Waves of the Same Type Wave Properties: Interference; Beats; Resonance Interference Anytime two waves of the same type (eg, two sound waves, two water waves) interact with one another, they combine together in the process called Interference. When this process occurs, the overlapping waves will combine their amplitudes at the point where the waves meet. When the crest of one wave meets the crest of a second wave, the two crests add together to create a larger combined crest. This is referred to as Constructive Interference; the net result is an increase in the overall amplitude of the waves (recall that amplitude refers to the height of a wave). Similarly, when the trough of one wave combines with the trough of another, we find that the two troughs add together to create a deeper combined trough. This is also Constructive Interference, because the amplitude has increased. In the case where the crest of one wave meets the trough of a second wave, they have a tendency to cancel each other out. This is referred to as Destructive Interference; the resulting amplitude of the two waves is the difference in their two amplitudes. If the two waves in question have the same amplitude and destructively interfere, then the two waves will completely cancel each other out at that point. If the amplitudes are different, then the resulting amplitude is equal to the difference in their amplitudes. The concept of Interference is very important in Acoustics. When an architectural firm is hired to construct a concert hall, it is carefully designed to minimize points where Destructive Interference can occur. Destructive interference is used intentionally in the construction of Active Noise Cancellation devices, such as headphones. In this case, a microphone detects surrounds noises and a speaker will then transmit a sound wave that is a mirror image of the incoming wave in order to cancel it out. Beats When two waves with different frequencies interfere, the resulting wave will oscillate between high and low amplitudes with a given frequency. This oscillation is referred to as Beats. In the diagram below, two sound waves are added together. One wave has a frequency of 10 Hz, while the other has a frequency of 12 Hz. Their sum (the resulting wave when they interfere) is shown in the bottom graph. Notice that the resulting wave rises and falls in a sinusoidal way; at some points, the interference is constructive; at other times, it is destructive. The net result is that the sound wave we hear (the sum of the two waves) will oscillate between loud and faint. The frequency of the Beat is equal to the difference in the frequency of the two initial waves. In this case, the sound wave we hear (the combination of the initial waves) will have a Beat Frequency of 2 Hz [12 Hz – 10 Hz]. Beats are used to tune musical instruments. When a piano tuner is tuning a piano, he or she will use a tuning fork (that puts out a pure sound frequency) and listen for beats between it and the vibrating string. When no beats occur, the piano is correctly tuned. The same is true of when a symphonic band tunes their instruments. Resonance When an object is disturbed in some way, it will have a tendency to vibrate at its so­called Natural Frequency, which can depend on a variety of factors. For instance, a violin string will have a Natural Frequency depending on its length, cross­sectional area, and tension. Anytime an object is forced to vibrate at its natural frequency, we say that the object is in Resonance. The result of a forced oscillation at Resonance is that the Amplitude of the oscillation will increase very dramatically, even if the force creating the disturbance is small. Imagine you are pushing someone in a swing; you will find that you get a large swing amplitude when you push in rhythm with (i.e., at the natural frequency of) the swing; this is exactly the concept of Resonance. You can achieve a fairly large amplitude of the swing with a fairly small push, so long as you push in rhythm. When you tune a radio receiver (say, in your car stereo) you are searching for the point where the receiver will resonate with an incoming radio wave. This is why you can clearly hear one station, as opposed to hearing all stations at the same time. When an acoustic guitar is played, the vibrating string causes the air in the body of the guitar to vibrate at the same frequency, producing the sound that we hear. You don’t hear the vibration of the string; the waves produced have too low an amplitude. But, when the air in the guitar’s body resonates at the same frequency as the string, the resulting amplitude is more than enough for you to hear. A potential negative result of Resonance is that the amplitude becomes too large, and the object will destroy itself. In one example, a troop of soldiers were marching over a bridge in­step; the soldiers just happened to be marching in time with the natural frequency of the bridge. As a result, the bridge began to wildly vibrate to the point that it collapsed. A similar event occurred in the 1940 collapse of the Tacoma Narrows Bridge in Washington State. This newly­opened bridge spanned a gorge across a river. On November 7, a 40 mph wind caused the bridge to begin vibrating at its natural frequency. As Resonance occurred, the amplitude of the vibrations increased to the point that the bridge literally tore itself apart, collapsing and falling to the water below..
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