Homework 4 solutions

Homework 4 solutions - WebAssign Problems 1. Suppose that...

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Unformatted text preview: WebAssign Problems 1. Suppose that you hear a clap of thunder 16.2 s after seeing the associated lightning stroke. The speed of sound waves in air is 343 m/s and the speed of light in air is 3.00 10 8 m/s. How far are you from the lightning stroke? Solution: Since light sound v v >> : ( ) ( ) 343 m s 16.2 s 5.56 km d = 2. A cowboy stands on horizontal ground between two parallel vertical cliffs. He is not midway between the cliffs. He fires a shot, and hears its echoes. The second echo arrives 1.92 s after the first, and 1.47 s before the third. Consider only the sound traveling parallel to the ground and reflecting from the cliffs. Take the speed of sound as 340 m/s. (a) What is the distance between the cliffs? (b) What If? If he can hear a fourth echo, how long after the third echo does it arrive? Solution: Let 1 x represent the cowboys distance from the nearer canyon wall and 2 x his distance from the farther cliff. The sound for the first echo travels distance 1 2 x . For the second, 2 2 x . For the third, 1 2 2 2 x x + . For the fourth echo, 1 2 1 2 2 2 x x x + + . Then 2 1 2 2 1.92 s 340 m s x x- = and 1 2 2 2 2 2 1.47 s 340 m s x x x +- = . Thus 1 1 340 m s 1.47 s 250 m 2 x = = and 2 2 1.92 s 1.47 s 340 m s x = + ; 2 576 m x = . (a) So 1 2 826 m x x + = (b) ( ) 1 2 1 1 2 2 2 2 2 2 1.47 s 340 m s x x x x x + +- + = 3. An ultrasonic tape measure uses frequencies above 20 MHz to determine dimensions of structures such as buildings. It does this by emitting a pulse of ultrasound into air and then measuring the time for an echo to return from a reflecting surface whose distance away is to be measured. The distance is displayed as a digital read-out. For a tape measure that emits a pulse of ultrasound with a frequency of 22.0 MHz, (a) what is the distance to an object from which the echo pulse returns after 24.0 ms when the air temperature is 26 o C? (b) What should be the duration of the emitted pulse if it is to include 10 cycles of the ultrasonic wave? (c) What is the spatial length of such a pulse? Solution: The sound speed is 26 C 331 m s 1 346 m s 273 C v = + = (a) Let t represent the time for the echo to return. Then 3 1 1 346 m s 24 10 s 4.16 m 2 2 d vt- = = = . (b) Let t represent the duration of the pulse: 6 10 10 10 10 0.455 s 22 10 1 s t v f f = = = = = . (c) ( ) 6 10 346 m s 10 10 0.157 m m 22 10 1 s v L f = = = = 4. A sinusoidal sound wave is described by the displacement wave function s ( x , t ) = (2.00 m)cos[(15.7 m 1 ) x (858 s 1 ) t ] (a) Find the amplitude, wavelength, and speed of this wave. (b) Determine the instantaneous displacement from equilibrium of the elements of air at the position x = 0.050 0 m at t = 3.00 ms. (c) Determine the maximum speed of the elements oscillatory motion....
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Homework 4 solutions - WebAssign Problems 1. Suppose that...

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