Four waves are described by the following equations, in which all distances are

Question

Four waves are described by the following equations, in which all distances are measured in centimeters and all times are measured in seconds:

PART A

Which of these waves travel in the exttip{+x}{+x} direction?

CHECK ALL THAT APPLY

Which of these waves travel in the exttip{+x}{+x} direction?

Check all that apply.

Check all that apply.

C

D

PART B

Which of these waves travel in the exttip{-x}{-x} direction?

CHECK ALL THAT APPLY

A

B

C

D

PART C

Which wave has the highest frequency? CHECK ONE

PART D

Which wave has the greatest wavelength? CHECK ONE

PART E

Which wave has the greatest speed? CHECK ONE

C

D

PART B

Which of these waves travel in the exttip{-x}{-x} direction?

CHECK ALL THAT APPLY

A

B

C

D

PART C

Which wave has the highest frequency? CHECK ONE

PART D

Which wave has the greatest wavelength? CHECK ONE

PART E

Which wave has the greatest speed? CHECK ONE

Explanation / Answer

Ya= 10 cos( 3x- 4t)

Yb= 10 cos( 5x+ 4t)

Yc= 20 cos( -10x+ 60t)

Yc= 20 cos( -4x - 20t)

Part A

For a particular section of the wave which is moving in any direction, the phase must be constant. So, if the equation says y(x,t)=Acos(t+x+)y(x,t)=Acos(t+x+), the term inside the cosine must be constant. Hence, if time increases, xx must decrease to make that happen. That makes the location of the section of wave in consideration and the wave move in negative direction.

Opposite of above happens when the equation says y(x,t)=Acos(tx+)y(x,t)=Acos(tx+). If t increase, xxmust increase to make up for it. That makes a wave moving in positive direction.

Therefore, Ya and Yc travel in x positive direction

Part B

Yb and Yd travel in negative x direction

Part C

Yc because it has the highest angular frecuency =60

Part D

Ya has a coefficient 3 for x, which is the smallest k=1/ , =1/k, when k (x coefficient) is smaller, the wavelenght () is greater.

Part E

The greater speed correspond to the wave that has the greater ratio of the coefficients of t and x

v=/k = 60/10 = 6 cm/s wave Yc

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