PHYS2001_Ch. 16

PHYS2001_Ch. 16 - Ch. 16 Sound and Waves 16.1 The Nature of...

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Ch. 16 Sound and Waves 16.1 The Nature of Waves Properties of waves: 1. A wave is a traveling disturbance. 2. Waves carry energy from place to place. We will study two types of waves in this chapter: 1. Transverse Waves : The disturbance (or oscillation) in the wave is perpendicular to the direction of wave propagation. 2. Longitudinal Waves : The disturbance (or oscillation) in the wave is along the direction of wave propagation. D 16.2 Periodic Waves A periodic wave is cyclic. It repeats over and over. Let’s take a look at a transverse wave on a slinky, for example. Transverse Wave Compression Wave
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Transverse Wave Let’s make a plot of the vertical position of the slinky as a function of distance: The disturbance or oscillation has a maximum displacement both above and below the equilibrium position of the slinky. This is the Amplitude (A). The horizontal length of 1 cycle of the wave is called the Wavelength ( λ ). Now let’s make a plot of the vertical position of a point on the slinky as a function of time: The time required for one complete up-and- down cycle is called the Period ( T ). And we know from our previous work, that the period of the motion is related to the Frequency ( f ) : T f 1 = [cycles/s] = [Hz]
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A very simple and important relationship exists between the frequency and wavelength of a wave: Time Cycles = f Cycle Distance = λ or Now let’s look at the product of the frequency and wavelength: Cycle Distance Time Cycles × = f v = = Velocity f v = T v = Example : A longitudinal wave with a frequency of 3.0 Hz takes 1.7 s to travel the distance of a 2.5-m slinky. What is the wavelength of the wave? f v = f t d = m 49 . 0 ) 0 . 3 )( 7 . 1 ( 5 . 2 = =
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16.3 The Speed of a Wave Let’s look at a transverse wave propagating toward a wall: The speed of the wave will depend on how fast the segment of string at point 1 can pull up on the segment of string at point 2. By Newton’s 2 nd Law, F = ma , so a greater force means a greater acceleration, and thus a faster moving wave. But what is the force in this case for the wave on a string??? It’s the tension in the string! Thus, the greater the tension in the string, the faster waves will move on the string. But, the acceleration of each mass segment of string, also depends on the mass of the string. The lighter each mass segment of string, the greater the acceleration, and thus speed. For a continuous medium, like a string, rope, wire or cable, we can use Mass Density.
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Length Mass Density Mass = L M = ρ For small amplitude waves propagating along a continuous media, the speed of the wave is given by: F v = m FL = F is the tension force along the media (string, rope, etc.) Example : To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.125-kg ball from the end of a wire. The wire has a length of 0.75 m and a linear density of 7.9 × 10 -4 kg/m. The astronaut measures the time it takes a transverse wave pulse to travel the length of the wire. The measured time was 0.064 s. Assume the mass of the wire is negligible compared to the mass of the ball, and calculate the acceleration due to gravity on this planet.
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16.5 Sound Waves
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This note was uploaded on 09/22/2009 for the course PHYS 2001 taught by Professor Sprunger during the Spring '08 term at LSU.

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PHYS2001_Ch. 16 - Ch. 16 Sound and Waves 16.1 The Nature of...

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