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# A water wave traveling in a straight line on a lake is ISBN: 9780321675460 31

## Solution for problem 10E Chapter 15

University Physics | 13th Edition

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Problem 10E

A water wave traveling in a straight line on a lake is described by the equation y(x , t) = (2.75 cm) cos(0.410 rad/cm x + 6.20 rad/s t) where y is the displacement perpendicular to the undisturbed surface of the lake. (a) How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor, and what horizontal distance does the wave crest travel in that time? (b) What are the wave number and the number of waves per second that pass the fisherman? (c) How fast does a wave crest travel past the fisherman, and what is the maximum speed of his cork floater as the wave causes it to bob up and down?

Step-by-Step Solution:

Solution 10E Step 1 of 7: For the given water wave traveling in a straight line on a lake is described by the equation y(x , t) = (2.75 cm) cos(0.410 rad/cm x + 6.20 rad/s t) From the above equation, Amplitude, A= 2.75 cm 1 Wave number, k=0.410 cm 1 Angular frequency, =6.2 s Step 2 of 7: (a) How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor, and what horizontal distance does the wave crest travel in that time To calculate the time taken for one complete wave pattern to go past a fisherman in a boat at anchor Using T= f where f is frequency Using f= T= 2 2 Substituting =6.2 s1 T= 2× 6.2 s T=1.012 sec Therefore, time taken to reach the fisherman is 1.012 s. Step 3 of 7: To calculate the horizontal distance the wave crest travel in that time Using = 2 k 1 2 Substituting k=0.410 cm = 0.410 cm = 15.31 cm Therefore, the wave crest travels 15.31 cm in that time. Step 4 of 7: (b) What are the wave number and the number of waves per second that pass the fisherman 1 Wave number, k=0.410 cm To calculate the number of waves per second that pass the fisherman, Using f= 2 1 Substituting =6.2 s 1 f= 2×3.14 f= 0.987 Hz Therefore, the number of waves that passes fishermen in one second is 0.987 Hz.

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##### ISBN: 9780321675460

This full solution covers the following key subjects: wave, fisherman, RAD, Travel, past. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “A water wave traveling in a straight line on a lake is described by the equation y(x , t) = (2.75 cm) cos(0.410 rad/cm x + 6.20 rad/s t) where y is the displacement perpendicular to the undisturbed surface of the lake. (a) How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor, and what horizontal distance does the wave crest travel in that time? (b) What are the wave number and the number of waves per second that pass the fisherman? (c) How fast does a wave crest travel past the fisherman, and what is the maximum speed of his cork floater as the wave causes it to bob up and down?” is broken down into a number of easy to follow steps, and 124 words. The full step-by-step solution to problem: 10E from chapter: 15 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. Since the solution to 10E from 15 chapter was answered, more than 2004 students have viewed the full step-by-step answer. University Physics was written by and is associated to the ISBN: 9780321675460. This textbook survival guide was created for the textbook: University Physics, edition: 13.

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