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Chapter 17, Problem 10P

(a)

To determine

To draw: The graphs showing y as a function of x for five instants t=0 , t=5ms , t=10ms , t=15ms and t=20ms .

(a)

Expert Solution
Check Mark

Answer to Problem 10P

The graph of y as a function of x at an instant t=0 is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  1

Figure (1)

The graph of y as a function of x at an instant t=5ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  2

Figure (2)

The graph of y as a function of x at an instant t=10ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  3

Figure (3)

The graph of y as a function of x at an instant t=15ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  4

Figure (4)

The graph of y as a function of x at an instant t=20ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  5

Figure (5)

Explanation of Solution

Introduction:

The values of y varies in sinusoidal form. Initially it increases from zero to its maximum value and then decreases from maximum value to zero. This phenomenon gets repeated in periodic form.

Given info: The sinusoidal waves function is,

y=6sin(π2x)cos(100πt) . (1)

For t=0 :

Substitute 0 for t in the equation (1).

y=6sin(π2x)cos(100π×0)=6sin(π2x)cos(0)=6sin(π2x)×1=6sin(π2x)

The graph of y as a function of x at an instant t=0 is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  6

Figure (1)

For t=5ms :

Substitute 5ms for t in the equation (1).

y=6sin(π2x)cos(100π×(5ms))=6sin(π2x)cos(100π×(5×103s))=6sin(π2x)×cos(0.5π)=0

The graph of y as a function of x at an instant t=5ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  7

Figure (2)

For t=10ms :

Substitute 10ms for t in the equation (1).

y=6sin(π2x)cos(100π×10ms)=6sin(π2x)cos(100π×10×103s)=6sin(π2x)×cos(π)=6sin(π2x)

The graph of y as a function of x at an instant t=10ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  8

Figure (3)

For t=15ms :

Substitute 15ms for t in the equation (1).

y=6sin(π2x)cos(100π×15ms)=6sin(π2x)cos(100π×15×103s)=6sin(π2x)×cos(1.5π)=0

The graph of y as a function of x at an instant t=15ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  9

Figure (4)

For t=20ms :

Substitute 20ms for t in the equation (1).

y=6sin(π2x)cos(100π×20ms)=6sin(π2x)cos(100π×20×103s)=6sin(π2x)×cos(2π)=6sin(π2x)

The graph of y as a function of x at an instant t=20ms is shown below.

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term, Chapter 17, Problem 10P , additional homework tip  10

Figure (5)

(b)

To determine

The wavelength of the wave using the graph of y as a function of x .

(b)

Expert Solution
Check Mark

Answer to Problem 10P

The wavelength of the wave is 4m .

Explanation of Solution

Given info: The sinusoidal waves function is y=6sin(π2x)cos(100πt) .

The distance between the two-crest point or two trough point is called the wavelength of the wave.

From the figure (1), the distance between the two crest point is 4m . Therefore, the wavelength of the wave is,

λ=4m

Conclusion:

Therefore, the wavelength of the wave is 4m .

(c)

To determine

The frequency of the wave using the graph of y as a function of x .

(c)

Expert Solution
Check Mark

Answer to Problem 10P

The frequency of the wave is 50Hz .

Explanation of Solution

Given info: The sinusoidal waves function is y=6sin(π2x)cos(100πt) .

Compare the equation (1) with y=Asinkxcosωt .

ω=100π

The frequency of the wave is,

f=ω2π

Substitute 100π for ω in the above equation.

f=100π2π=50Hz

Conclusion:

Therefore, the frequency of the wave is 50Hz .

(d)

To determine

The wavelength of the wave using the equation of the wave.

(d)

Expert Solution
Check Mark

Answer to Problem 10P

The wavelength of the wave is 4m .

Explanation of Solution

Given info: The sinusoidal waves function is y=6sin(π2x)cos(100πt) .

Compare the equation (1) with y=Asinkxcosωt .

k=π2

The frequency of the wave is,

λ=2πk

Substitute π2 for k in the above equation.

λ=2π(π2)=4m

Conclusion:

Therefore, the wavelength of the wave is 4m .

(e)

To determine

The frequency of the wave using the equation of the wave.

(e)

Expert Solution
Check Mark

Answer to Problem 10P

The frequency of the wave is 50Hz .

Explanation of Solution

Given info: The sinusoidal waves function is y=6sin(π2x)cos(100πt) .

Compare the equation (1) with y=Asinkxcosωt .

ω=100π

The frequency of the wave is,

f=ω2π

Substitute 100π for ω in the above equation.

f=100π2π=50Hz

Conclusion:

Therefore, the frequency of the wave is 50Hz .

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Chapter 17 Solutions

Bundle: Physics For Scientists And Engineers With Modern Physics, 10th + Webassign Printed Access Card For Serway/jewett's Physics For Scientists And Engineers, 10th, Multi-term

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