The value of the sum of two wave functions y 1 + y 2 at given points.

Question

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Answer 1

Question

Chapter 14, Problem 5P

(a)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(a)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 1 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 1 s for t in above expression to find y .

y=3.0 cos(4.0×1 cm−1.6×1 s)+4.0 sin(5.0×1 cm−2.0×1 s)=−1.647 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

(b)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(b)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 0.500 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 0.500 s for t to find the y .

y=3.0 cos(4.0×1 cm−1.6×0.500 s)+4.0 sin(5.0×1 cm−2.0×0.500 s)=−6.022 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

(c)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(c)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Explanation of Solution

Given info:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 0.500 cm and time of the wave function is 0 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) ,

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 0.500 cm for x and 0 s for t to find the y .

y=3.0 cos(4.0×0.500 cm−1.6×0 s)+4.0 sin(5.0×0.500 cm−2.0×0 s)=1.15 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

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Answer 2

Question

Chapter 14, Problem 5P

(a)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(a)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 1 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 1 s for t in above expression to find y .

y=3.0 cos(4.0×1 cm−1.6×1 s)+4.0 sin(5.0×1 cm−2.0×1 s)=−1.647 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

(b)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(b)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 0.500 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 0.500 s for t to find the y .

y=3.0 cos(4.0×1 cm−1.6×0.500 s)+4.0 sin(5.0×1 cm−2.0×0.500 s)=−6.022 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

(c)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(c)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Explanation of Solution

Given info:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 0.500 cm and time of the wave function is 0 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) ,

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 0.500 cm for x and 0 s for t to find the y .

y=3.0 cos(4.0×0.500 cm−1.6×0 s)+4.0 sin(5.0×0.500 cm−2.0×0 s)=1.15 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

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Answer 3

Question

Chapter 14, Problem 5P

(a)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(a)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 1 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 1 s for t in above expression to find y .

y=3.0 cos(4.0×1 cm−1.6×1 s)+4.0 sin(5.0×1 cm−2.0×1 s)=−1.647 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

(b)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(b)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 0.500 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 0.500 s for t to find the y .

y=3.0 cos(4.0×1 cm−1.6×0.500 s)+4.0 sin(5.0×1 cm−2.0×0.500 s)=−6.022 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

(c)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(c)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Explanation of Solution

Given info:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 0.500 cm and time of the wave function is 0 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) ,

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 0.500 cm for x and 0 s for t to find the y .

y=3.0 cos(4.0×0.500 cm−1.6×0 s)+4.0 sin(5.0×0.500 cm−2.0×0 s)=1.15 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

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Answer 4

Question

Chapter 14, Problem 5P

(a)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(a)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 1 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 1 s for t in above expression to find y .

y=3.0 cos(4.0×1 cm−1.6×1 s)+4.0 sin(5.0×1 cm−2.0×1 s)=−1.647 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

(b)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(b)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 0.500 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 0.500 s for t to find the y .

y=3.0 cos(4.0×1 cm−1.6×0.500 s)+4.0 sin(5.0×1 cm−2.0×0.500 s)=−6.022 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

(c)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(c)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Explanation of Solution

Given info:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 0.500 cm and time of the wave function is 0 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) ,

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 0.500 cm for x and 0 s for t to find the y .

y=3.0 cos(4.0×0.500 cm−1.6×0 s)+4.0 sin(5.0×0.500 cm−2.0×0 s)=1.15 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

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Answer 5

Chapter 14, Problem 5P

(a)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(a)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 1 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 1 s for t in above expression to find y .

y=3.0 cos(4.0×1 cm−1.6×1 s)+4.0 sin(5.0×1 cm−2.0×1 s)=−1.647 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

(b)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(b)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 0.500 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 0.500 s for t to find the y .

y=3.0 cos(4.0×1 cm−1.6×0.500 s)+4.0 sin(5.0×1 cm−2.0×0.500 s)=−6.022 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

(c)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(c)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Explanation of Solution

Given info:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 0.500 cm and time of the wave function is 0 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) ,

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 0.500 cm for x and 0 s for t to find the y .

y=3.0 cos(4.0×0.500 cm−1.6×0 s)+4.0 sin(5.0×0.500 cm−2.0×0 s)=1.15 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Answer 6

Chapter 14, Problem 5P

(a)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(a)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 1 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 1 s for t in above expression to find y .

y=3.0 cos(4.0×1 cm−1.6×1 s)+4.0 sin(5.0×1 cm−2.0×1 s)=−1.647 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Answer 7

Chapter 14, Problem 5P

(a)

To determine

The value of the sum of two wave functions y1+y2 at given points.

Answer 8

(a)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 1 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 1 s for t in above expression to find y .

y=3.0 cos(4.0×1 cm−1.6×1 s)+4.0 sin(5.0×1 cm−2.0×1 s)=−1.647 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −1.647 cm .

Answer 13

(b)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(b)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 0.500 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 0.500 s for t to find the y .

y=3.0 cos(4.0×1 cm−1.6×0.500 s)+4.0 sin(5.0×1 cm−2.0×0.500 s)=−6.022 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Answer 14

(b)

To determine

The value of the sum of two wave functions y1+y2 at given points.

Answer 15

(b)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 1 cm and time of the wave function is 0.500 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) .

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 1 cm for x and 0.500 s for t to find the y .

y=3.0 cos(4.0×1 cm−1.6×0.500 s)+4.0 sin(5.0×1 cm−2.0×0.500 s)=−6.022 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is −6.022 cm .

Answer 20

(c)

To determine

The value of the sum of two wave functions y1+y2 at given points.

(c)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Explanation of Solution

Given info:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 0.500 cm and time of the wave function is 0 s .

The sum of two wave functions is,

y=y1+y2

y is the sum of the two wave functions.
y1 is the first wave function.
y2 is second wave function.

Substitute 3.0 cos(4.0x−1.6t) for y1 and 4.0 sin(5.0x−2.0t) ,

y=3.0 cos(4.0x−1.6t)+4.0 sin(5.0x−2.0t)

Substitute 0.500 cm for x and 0 s for t to find the y .

y=3.0 cos(4.0×0.500 cm−1.6×0 s)+4.0 sin(5.0×0.500 cm−2.0×0 s)=1.15 cm

Conclusion:

Therefore, the value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Answer 21

(c)

To determine

The value of the sum of two wave functions y1+y2 at given points.

Answer 22

(c)

Expert Solution

Answer to Problem 5P

The value of the sum of two wave functions y1+y2 at given points is 1.15 cm .

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given info:The first wave function is 3.0 cos(4.0x−1.6t) , the second wave function is 4.0 sin(5.0x−2.0t) , the position of the element is 0.500 cm and time of the wave function is 0 s .