Explanation Consider the given figure, Figure-(1) Consider figure (1), the amplitude of the wave is maximum at t = 0 s and x = 0 cm with the value 3.5 cm . One cycle is completed at x = 20 cm . Thus, the wavelength of the wave is 20 cm . The maxima has moved from x = 0 cm to nearly x = 12 cm in time t = 0.80 s . The relation between velocity, distance and time is, v = x t (I) Here, v is the velocity, x is the distance and t is the time. Write relation to calculate angular frequency. ω = v k (II) Here, ω is the angular frequency, v is the velocity and k is the wave number. Write the expression to calculate k . k = 2 π λ (III) Here, λ is the wavelength of the wave. Consider the figure (1); the wave is moving towards right and the maximum displacement is when t = 0 s and x = 0 cm . Thus, for this condition represent the wave equation using cosine function as, D ( x , t ) = A cos ( k x − ω t ) (IV) Conclusion: Substitute 12 cm for x and 0

Modified Mastering Physics without Pearson eText-- Instant Access -- for Physics for Scientists & Engineers with Modern Physics

5th Edition

ISBN: 9780134402659

Author: GIANCOLI, Douglas

Publisher: PEARSON

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Equation of Waves

Wave is an oscillation or disturbance traveling in a medium. It performs the transportation of energy but does not carry any matter. This motion of waves will transport fuel in a medium without permanent transfer of mass (particle).

Question

Chapter 15, Problem 92GP

To determine

The mathematical representation of the wave.

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Chapter 15, Problem 91GP

Chapter 15, Problem 93GP

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Chapter 15 Solutions

Modified Mastering Physics without Pearson eText-- Instant Access -- for Physics for Scientists & Engineers with Modern Physics

Ch. 15.1 - Prob. 1AE Ch. 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. 1Q Ch. 15 - Explain the difference between the speed of a...Ch. 15 - Prob. 3Q Ch. 15 - What kind of waves do you think will travel down a...Ch. 15 - Prob. 5Q Ch. 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. 9Q Ch. 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. 14Q Ch. 15 - Prob. 15Q Ch. 15 - Prob. 16Q Ch. 15 - Prob. 17Q Ch. 15 - Prob. 18Q Ch. 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. 22Q Ch. 15 - Prob. 1MCQ Ch. 15 - Prob. 2MCQ Ch. 15 - Prob. 3MCQ Ch. 15 - Prob. 4MCQ Ch. 15 - Prob. 5MCQ Ch. 15 - Prob. 6MCQ Ch. 15 - Prob. 7MCQ Ch. 15 - Prob. 8MCQ Ch. 15 - Prob. 9MCQ Ch. 15 - Prob. 10MCQ Ch. 15 - Prob. 11MCQ Ch. 15 - Prob. 1P Ch. 15 - Prob. 2P Ch. 15 - (I) Calculate the speed of longitudinal waves in...Ch. 15 - (1) AM radio signals have frequencies between 550...Ch. 15 - Prob. 5P Ch. 15 - Prob. 6P Ch. 15 - Prob. 7P Ch. 15 - Prob. 8P Ch. 15 - Prob. 9P Ch. 15 - Prob. 10P Ch. 15 - Prob. 11P Ch. 15 - Prob. 12P Ch. 15 - Prob. 13P Ch. 15 - Prob. 14P Ch. 15 - Prob. 15P Ch. 15 - Prob. 16P Ch. 15 - Prob. 17P Ch. 15 - Prob. 18P Ch. 15 - Prob. 19P Ch. 15 - (II) Show that the intensity of a wave is equal to...Ch. 15 - Prob. 21P Ch. 15 - Prob. 22P Ch. 15 - Prob. 23P Ch. 15 - Prob. 24P Ch. 15 - Prob. 25P Ch. 15 - Prob. 26P Ch. 15 - (II) A transverse wave pulse travels to the right...Ch. 15 - Prob. 28P Ch. 15 - Prob. 29P Ch. 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. 32P Ch. 15 - Prob. 33P Ch. 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. 36P Ch. 15 - Prob. 37P Ch. 15 - Prob. 38P Ch. 15 - Prob. 39P Ch. 15 - Prob. 40P Ch. 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. 44P Ch. 15 - Prob. 45P Ch. 15 - (I) If a violin string vibrates at 294 Hz as its...Ch. 15 - Prob. 47P Ch. 15 - Prob. 48P Ch. 15 - (II) The velocity of waves on a string is 96 m/s....Ch. 15 - Prob. 50P Ch. 15 - Prob. 51P Ch. 15 - Prob. 52P Ch. 15 - Prob. 53P Ch. 15 - (II) In Problem 52, Fig. 1537, the length of the...Ch. 15 - Prob. 55P Ch. 15 - Prob. 56P Ch. 15 - Prob. 57P Ch. 15 - Prob. 58P Ch. 15 - (II) Plot the two waves given in Problem 58 and...Ch. 15 - Prob. 60P Ch. 15 - Prob. 61P Ch. 15 - (II) Two oppositely directed traveling waves given...Ch. 15 - Prob. 63P Ch. 15 - Prob. 64P Ch. 15 - (I) An earthquake P wave traveling 8.0 km/s...Ch. 15 - Prob. 67P Ch. 15 - (I) Water waves approach an underwater shelf where...Ch. 15 - Prob. 69P Ch. 15 - Prob. 70P Ch. 15 - Prob. 71GP Ch. 15 - Prob. 72GP Ch. 15 - (II) Seismic reflection prospecting is commonly...Ch. 15 - Prob. 74GP Ch. 15 - A bug on the surface of a pond is observed to move...Ch. 15 - Prob. 76GP Ch. 15 - Prob. 77GP Ch. 15 - Prob. 78GP Ch. 15 - Prob. 79GP Ch. 15 - Prob. 80GP Ch. 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. 83GP Ch. 15 - Prob. 84GP Ch. 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. 87GP Ch. 15 - Prob. 88GP Ch. 15 - Prob. 90GP Ch. 15 - A highway overpass was observed to resonate as one...Ch. 15 - Prob. 92GP Ch. 15 - Estimate the average power of a water wave when it...Ch. 15 - Prob. 94GP Ch. 15 - Two wave pulses are traveling in opposite...Ch. 15 - Prob. 96GP

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The mathematical representation of the wave.

Solution Summary: The author explains how the wave can be represented mathematically using a cosine function.

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The mathematical representation of the wave.

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Chapter 15 Solutions