Physics 4C Spring 2016 Test 3

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1 Physics 4C Spring 016 Test 3 Name: June 1, 016 Please show your work! Answers are not complete without clear reasoning. When asked for an expression, you must gie your answer in terms of the ariables gien in the question and/or fundamental constants. Answer as many questions as you can, in any order. Calculators are allowed. Books and notes are not allowed. Use any blank space to answer questions, but please make sure it is clear which question your answer refers to. g = 9.8 ms c = m/s ρ air = 1.0 kg m 3 (sea leel, 0 C I 0 = W m = (331 m/s 1 + T Cel 73 B = P V/V i y(t = n=1 ( An sin(πnft + B n cos(πnft sin θ + cos θ = 1 sin(α ± β = sin α cos β ± cos α sin β cos(α ± β = cos α cos β sin α sin β sin α + sin β = cos ( ( α β sin α+β cos α + cos β = cos ( α β sin ( θ + π = cos θ cos ( θ + π = sin θ Trigonometric Identities cos ( α+β 1

2 y(x, t at t 5 0. (b Sketch y(x, t at y 1x, t sin a10pt 3px 1 b 4 are the graph in part (b with that plain similarities and differences. (a What are the speed and direction of trael of the ae moed between graph (a and wae? (b What is the ertical position of an element of 1. The string shownthe is drien string at sinusoidally t 5 0, x at m? a frequency What are (c ofthe 6.00 waelength 10.0and cm, (d and the the frequency wae speed of the wae? is = (e 5.0 What m/s. is Furthermore, the Hz. The amplitude of the motion is A = e pulse in a wire is described by the wae is such that the y = maximum 0 at x = transerse 0 and t = speed 0. of an element of the string? x (a Determine 10. the When angular a particular frequency wire for is ibrating this wae. with [a pts] frequency W of 4.00 Hz, a transerse wae of waelength 60.0 cm meters. If the pulse is (b traeling Determine the is produced. wae number Determine for this the wae. speed of [ waes pts] along the ion with a speed of 4.50 m/s, write (c Write an expression wire. that describes this pulse. for the wae function. [ pts] 11. The string shown in Figure P16.11 is drien at a fre- maximum of 5.00 transerse Hz. The amplitude speed of of an the element motion is of A the 5 string. [3 pts] B on (d Path of B Calculate thequency W Earth Rayleigh wae (e Calculate the1.0 maximum cm, and transerse the wae speed acceleration is of m/s. an element Furthermore, the wae is such that y 5 0 at x 5 0 and t 5 0. gitude of the string. [3 pts] atitude (f Considering the Determine acceleration (a the of angular element frequency of the and string, (b the wae show that the transerse P16.4. Path of motion of each number element for this simple wae. (c harmonic Write an motion. expression [ for pts] the ake at P wae wae function. Calculate (d the maximum transerse P wae 60.0 (g Suppose A the speed stringand has(e a the length maximum 1.00 mtranserse and a mass acceleration of 0.0of g. What is the power B by of this wae? an [4element pts] of the string. rough Figure P16.4 th at a A 80 km/s. The earthquake also radithat traels at 4.50 km/s. In addition S yleigh waes are a third type of seisalong the surface of the Earth rather Figure P16.11 lk of the Earth. (a Which of these 1. Consider the sinusoidal wae of Example 16. with the ries at B first? (b What is the time wae function he arrials of these two waes at B? y cos (15.7x 50.3t odel: Traeling Wae by y sin (kx t, where 3.6 rad/s, x and y are in meters, s. Determine (a the amplitude, (c the frequency, and (d the speed string is held under constant ten- -iew snapshot of a sinusoidal wae in diagrams in the text. (b Immeam (a, draw the same wae at a e-quarter of the period of the wae. ae with an amplitude 1.5 times e in diagram (a. (d Next, draw a the one in your diagram (a just by 1.5 times larger. (e Finally, draw a that in diagram (a just by haing s larger. where x and y are in meters and t is in seconds. At a certain instant, let point A be at the origin and point B be the closest point to A along the x axis where the wae is 60.0 out of phase with A. What is the coordinate of B? 13. A sinusoidal wae of waelength.00 m and amplitude m traels on a string with a speed of 1.00 m/s to the right. At t 5 0, the left end of the string is at the origin. For this wae, find (a the frequency, (b the angular frequency, (c the angular wae number, and (d the wae function in SI units. Determine the equation of motion in SI units for (e the left end of the string and (f the point on the string at x m to the right of the left end. (g What is the maximum speed of any element of the string? 14. (a Plot y ersus t at x 5 0 for a sinusoidal wae of the Q/C form y cos (15.7x 50.3t, where x and y are in

3 . A pair of speakers facing each other generate identical sinusoidal waes with amplitudes P max and elocities in opposite directions. Together they produce the standing wae: P = ( P max S sin kx cos ωt S (a Show by substituting the standing wae gien aboe into the wae equation that it is a alid solution of the wae equation. [7 pts] (b The standing wae as it is written does not appear to hae a direct dependence on the ariables x and t only as (x t. Can it be written as a function of (x t? If so, show how. [4 pts] 3

4 3. Two adjacent natural frequencies of a double-open-ended organ pipe are determined to be 400 Hz and 450 Hz. (a Calculate the fundamental frequency. [4 pts] (b Calculate the length of this pipe. [3 pts] (c How many displacement nodes are there in this pipe in a standing wae at 400 Hz? [ pts] (d How many pressure nodes are there in this pipe at 400 Hz? [ pts] (Include any nodes at the ery end(s of the pipe in your count. 4

5 4. A student holds a tuning fork oscillating at a frequency f. He walks toward a wall at a constant speed u. Let the speed of sound in air be. (a Find an expression for the beat frequency he obseres between the tuning fork and its echo. [4 pts] (b The student continues to walk towards the wall with speed u, but gies the tuning fork to his friend. She walks away from the wall with the tuning fork at a speed u. What beat frequency does he hear now? [6 pts] Now the students take the tuning fork to an open field where there will not be any echos. (c One student stands still holding the ringing tuning fork. The other student stands a distance r away and measures the intensity of the sound, I. How much farther away must he walk so that the intensity drops to 1 I? [3 pts] (d What is the change in the sound leel he obseres as he walks that distance? [3 pts] 5

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10. Yes. Any function of (x - vt) will represent wave motion because it will satisfy the wave equation, Eq

10. Yes. Any function of (x - vt) will represent wave motion because it will satisfy the wave equation, Eq CHAPER 5: Wae Motion Responses to Questions 5. he speed of sound in air obeys the equation B. If the bulk modulus is approximately constant and the density of air decreases with temperature, then the speed