PHYSICS F/SCI.+ENGR.,CHAPTERS 1-37
5th Edition
ISBN: 9780134378060
Author: GIANCOLI
Publisher: RENT PEARS
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b) Two progressive waves y:(x,t) =Asin(2rAXwt) and y2(xt)
=Asin(2raX-wt-n2) travel in the same direction. Calculate the amplitude
and speed of the wave produced as a result of interference of these
two waves. Take the values as a=5cm, A=4m and w=31.4Hz.
If two travelling waves interfere to produce a standing wave described by: y(x,t) =
0.02sin(4Ttx)cos(120tt), then the wave functions of the two interfering waves
are:
y_1 (x,t) = 0.02sin(2rx - 60rt) and y_2 (x,t) = 0.02sin(2rtx + 60rt)
O y-1 (x,t) = 0.04sin(2rx - 60nt) and y_2 (x,t) = 0.04sin(2rx + 60nt)
O y-1 (x,t) = 0.02sin(4Tx - 120t) and y_2 (x,t) = 0.02sin(4Tx + 120nt)
O y-1 (x,t) = 0.01sin(4Tx - 120nt) and y_2 (x,t) = 0.01sin(4Tx + 120nt)
O y_1 (x,t) = 0.04sin(4Tx - 120nt) and y_2 (x,t) = 0.04sin(4Ttx + 120t)
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(b) 0.8 sec; 14 m/s
(c) 0.4 sec; 7 m/s
(d)0.8 sec; 3.5 m/s
4) Two identical sinusoidal waves travel in the same direction at the same speed with an amplitude A. The
phase difference between the two waves is o = 69.8°. The amplitude of the resultant wave, Aresultant»
is increased with respect to the amplitude of the individual waves, A, by:
(a) 18%
(b) 64%
(c) 82%
(d) 164%
5) Two identical sinusoidal waves with frequency of 20 Hz travel in the same đirection at the same speen
The two waves originate from the same point but with a time difference At. The amplitude of th
AV3. The minimum possible time difference between the starting moments
resultant wave is Ares
the two waves is, At =:
(a) 1/120 sec
(b)0477 sec
(c) 1/80 sec
(d)0.716 sec
rleueths of 2.5 m travel in the same direction with the
Ih difference. Wave-1 tra
Chapter 15 Solutions
PHYSICS F/SCI.+ENGR.,CHAPTERS 1-37
Ch. 15.1 - Prob. 1AECh. 15.1 - You notice a water Wave pass by the end of a pier...Ch. 15.2 - A wave starts at the left end of a long cord (see...Ch. 15.4 - A wave is given by D(x, t) = (5.0 mm) sin(2.0x ...Ch. 15 - Prob. 1QCh. 15 - Explain the difference between the speed of a...Ch. 15 - Prob. 3QCh. 15 - What kind of waves do you think will travel down a...Ch. 15 - Prob. 5QCh. 15 - Prob. 6Q
Ch. 15 - The speed of sound in most solids is somewhat...Ch. 15 - Give two reasons why circular water waves decrease...Ch. 15 - Prob. 9QCh. 15 - Will any function of (x t)see Eq. 1514represent a...Ch. 15 - When a sinusoidal wave crosses the boundary...Ch. 15 - If a sinusoidal wave on a two-section cord (Fig....Ch. 15 - Is energy always conserved when two waves...Ch. 15 - Prob. 14QCh. 15 - Prob. 15QCh. 15 - Prob. 16QCh. 15 - Prob. 17QCh. 15 - Prob. 18QCh. 15 - When a standing wave exists on a string, the...Ch. 15 - When a cord is vibrated as in Fig. 1525 by hand or...Ch. 15 - AM radio signals can usually be heard behind a...Ch. 15 - Prob. 22QCh. 15 - Prob. 1MCQCh. 15 - Prob. 2MCQCh. 15 - Prob. 3MCQCh. 15 - Prob. 4MCQCh. 15 - Prob. 5MCQCh. 15 - Prob. 6MCQCh. 15 - Prob. 7MCQCh. 15 - Prob. 8MCQCh. 15 - Prob. 9MCQCh. 15 - Prob. 10MCQCh. 15 - Prob. 11MCQCh. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - (I) Calculate the speed of longitudinal waves in...Ch. 15 - (1) AM radio signals have frequencies between 550...Ch. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10PCh. 15 - Prob. 11PCh. 15 - Prob. 12PCh. 15 - Prob. 13PCh. 15 - Prob. 14PCh. 15 - Prob. 15PCh. 15 - Prob. 16PCh. 15 - Prob. 17PCh. 15 - Prob. 18PCh. 15 - Prob. 19PCh. 15 - (II) Show that the intensity of a wave is equal to...Ch. 15 - Prob. 21PCh. 15 - Prob. 22PCh. 15 - Prob. 23PCh. 15 - Prob. 24PCh. 15 - Prob. 25PCh. 15 - Prob. 26PCh. 15 - (II) A transverse wave pulse travels to the right...Ch. 15 - Prob. 28PCh. 15 - Prob. 29PCh. 15 - (II) Write the equation for the wave in Problem 28...Ch. 15 - (II) A sinusoidal wave traveling on a string in...Ch. 15 - Prob. 32PCh. 15 - Prob. 33PCh. 15 - (II) Determine if the function D = A sin k x cos t...Ch. 15 - (II) Show by direct substitution that the...Ch. 15 - Prob. 36PCh. 15 - Prob. 37PCh. 15 - Prob. 38PCh. 15 - Prob. 39PCh. 15 - Prob. 40PCh. 15 - (II) A cord has two sections with linear densities...Ch. 15 - (III) A cord stretched to a tension FT consists of...Ch. 15 - (I) The two pulses shown in Fig. 1536 are moving...Ch. 15 - Prob. 44PCh. 15 - Prob. 45PCh. 15 - (I) If a violin string vibrates at 294 Hz as its...Ch. 15 - Prob. 47PCh. 15 - Prob. 48PCh. 15 - (II) The velocity of waves on a string is 96 m/s....Ch. 15 - Prob. 50PCh. 15 - Prob. 51PCh. 15 - Prob. 52PCh. 15 - Prob. 53PCh. 15 - (II) In Problem 52, Fig. 1537, the length of the...Ch. 15 - Prob. 55PCh. 15 - Prob. 56PCh. 15 - Prob. 57PCh. 15 - Prob. 58PCh. 15 - (II) Plot the two waves given in Problem 58 and...Ch. 15 - Prob. 60PCh. 15 - Prob. 61PCh. 15 - (II) Two oppositely directed traveling waves given...Ch. 15 - Prob. 63PCh. 15 - Prob. 64PCh. 15 - (I) An earthquake P wave traveling 8.0 km/s...Ch. 15 - Prob. 67PCh. 15 - (I) Water waves approach an underwater shelf where...Ch. 15 - Prob. 69PCh. 15 - Prob. 70PCh. 15 - Prob. 71GPCh. 15 - Prob. 72GPCh. 15 - (II) Seismic reflection prospecting is commonly...Ch. 15 - Prob. 74GPCh. 15 - A bug on the surface of a pond is observed to move...Ch. 15 - Prob. 76GPCh. 15 - Prob. 77GPCh. 15 - Prob. 78GPCh. 15 - Prob. 79GPCh. 15 - Prob. 80GPCh. 15 - A transverse wave pulse travels to the right along...Ch. 15 - (a) Show that if the tension in a stretched string...Ch. 15 - Prob. 83GPCh. 15 - Prob. 84GPCh. 15 - Two strings on a musical instrument are tuned to...Ch. 15 - The ripples in a certain groove 10.8 cm from the...Ch. 15 - Prob. 87GPCh. 15 - Prob. 88GPCh. 15 - Prob. 90GPCh. 15 - A highway overpass was observed to resonate as one...Ch. 15 - Prob. 92GPCh. 15 - Estimate the average power of a water wave when it...Ch. 15 - Prob. 94GPCh. 15 - Two wave pulses are traveling in opposite...Ch. 15 - Prob. 96GP
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- What is the necessary condition on the path length difference between two waves that interfere (a) constructively and (b) destructively?arrow_forwardTwo sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is =0.075 kg/m and the tension in the string is FT=5.00 N. The time interval between instances of total destructive interference is t=0.13 s. What is the wavelength of the waves?arrow_forwardTwo sources as in phase and emit waves with =0.42 m. Determine whether constructive or destructive interference occurs at points whose distances from the two sources are (a) 0.84 and 0.42 m, (b) 0.21 and 0.42 m, (c) 1.26 and 0.42 m, (d) 1.87 and 1.45 m, (e) 0.63 and 0.84 m and (f) 1.47 and 1.26 m.arrow_forward
- A string is fixed at both end. The mass of the string is 0.0090 kg and the length is 3.00 m. The string is under a tension of 200.00 N. The string is driven by a variable frequency source to produce standing waves on the string. Find the wavelengths and frequency of the first four modes of standing waves.arrow_forwardRank the waves represented by the following functions from the largest to the smallest according to (i) their amplitudes, (ii) their wavelengths, (iii) their frequencies, (iv) their periods, and (v) their speeds. If the values of a quantity are equal for two waves, show them as having equal rank. For all functions, x and y are in meters and t is in seconds. (a) y = 4 sin (3x 15t) (b) y = 6 cos (3x + 15t 2) (c) y = 8 sin (2x + 15t) (d) y = 8 cos (4x + 20t) (e) y = 7 sin (6x + 24t)arrow_forwardShow that the wave equation in one dimension 2fx2=1v22ft2 Is satisfied by any doubly differentiable function of either the form f(x — vt) or f(x + vt).arrow_forward
- Two waves Y1 = 3.6 sin (942 t –0.02512 x + 3n) and Y2 = 3.8 sin (942 t –0.02512 x + 47) interfere. Compute: (a) the frequency (f) of each wave, and (b) the wavelength (^.) of each wave (All quantities are in SI units)arrow_forward(a) Show that the function y(x, t) = x2 + v2t2is a solution to the wave equation. (b) Showthat the function in part (a) can be written as f(x + vt) + g(x − vt) and determine thefunctional forms for f and g. (c) What If? Repeat parts (a) and (b) for the function y(x,t) = sin (x) cos (vt)arrow_forward= A sin (x – wt) and y2(x, t) = A sin (x – wt –5) travel Two progressive waves y1(x, t) in the same direction. Calculate the amplitude and speed of the wave produced as a result of interference of these two waves. Take A = 5 cm, A = 4 m and w = 31.4 Hz. wt – 5) travelarrow_forward
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