Standing Waves

7 27 at the moment shown in figure 4 the string

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Unformatted text preview: 7 (27) At the moment shown in Figure 4, the string element Δl is moving in an arc of a circle. Thus, it has a centripetal acceleration toward the center of that circle given by (28) Equations (26)-(28) contain elements of Newton’s second law. Combining them in the form (29) ∆ ∆ (30) Solving equation (30) for the speed v yields (31) Equation (31) tells us: The speed of a wave along a stretched ideal string depends only on the tension and linear density of the string and NOT on the frequency of the wave. The frequency of a wave is fixed entirely by whatever generates the wave. The wavelength of the wave is then fixed by equation (23) in the form λ=v/f. 2.9 Sound Waves We saw in the previous sections, mechanical waves are waves that require a material medium to exist. There are two types of mechanical waves: Transverse waves involve oscillations perpendicular to the direction in which the waves travels; longitudinal waves involve oscillations parallel to the direction of wave travel. For the purpose of this lab, a sound wave is defined roughly as any longitudinal wave. Seismic prospecting teams use such waves to prove Earth’s crust contains oil. Ships carry sound-ranging gear (sonar) to detect underwater obstacles. Submarines use sound waves to stalk other submarines, largely by listening for the characteristic noises produced by the propulsion system. Figure 5 illustrates several ideas that we shall use in our discussions. Point S represents a tiny sound source, called a point source that emits sound waves in all directions. The wavefronts and rays indicate the direction of travel and the spread of the sound waves. Wavefronts are surfaces over which the oscillations due to the sound wave have the same value; such surfaces are represented by whole or partial circles in a two-dimensional drawing for a point source. Rays are directed lines perpendicular to the wavefronts that indicate the direction of travel of the wavefronts. The short double Figure 5 A sound wave travels from a point S arrows superimposed on the rays of Figure 5 indicate that the through a three-dimensional medium. Picture from Fundamentals of Physics 7th edition Wiley longitudinal oscillations of the air are parallel to the rays. Publishing Near a point source like that of Figure 5, the wavefronts are spherical and spread out in three-dimensions, and there the waves are said to the spherical. 8 As the wavefronts move outward and their radii become larger, their curvature decreases. Far from the source, we approximate the wavefronts are planes (or lines on two-dimensional drawings), and the waves are said to be plan...
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