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10.1 Properties of Waves

6 min readjune 11, 2020

Peter Apps

Peter Apps

Peter Apps

Peter Apps

Enduring Understanding 6.A 👨‍💻

A is a travelling disturbance that transfers and .

Essential Knowledge 6.A.1 🏘

Waves can propagate via different oscillation modes such as transverse and longitudinal.

Essential Knowledge 6.A.2 🏘

For propagation, mechanical waves require a .

Essential Knowledge 6.A.3 🏘

The is the maximum displacement of a from its equilibrium value.

Essential Knowledge 6.A.4 🏘

Classically, the carried by a depends on and increases with . Examples include sound waves.

Anatomy of a

A is a periodic disturbance, meaning that it repeats over and over in a predictable pattern. The disturbance can cause the particles of the material the is propagating through to vibrate either perpendicular or parallel to the direction of the ’s motion.

If the particles vibrate parallel to the direction of motion, the is longitudinal. If they vibrate perpendicular, the is transverse.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.12-6uZnEgO7swdl.png?alt=media&token=65a14fda-3e5e-4d4c-a7f2-a49908b05ba3

Image courtesy of Difference.Wiki.

Both types of waves have similar features:

- The height of the , measured from the equilibrium position.

- The also describes the amount of a transfers. The higher the , the larger the .

- The distance from one repeated unit to the next.

- On a Longitudinal this is from compression to compression or rarefaction to rarefaction.

- On a this is from crest to crest, or trough to trough.

Other key terms that have been covered in Unit 6 include:

- the time it takes for one cycle of a to occur

- the number of cycles of a in a given amount of time

The depends on the (material) that the is traveling through. In AP 1, we only deal with mechanical waves that require a to travel through (they can’t travel through empty space which is a vacuum). If you go ahead and take AP 2, you’ll learn about that can travel through empty space. In general terms, mechanical waves travel faster through denser materials, or when the tension in the material is greater. You can mess around with this concept by taking a look at the PhET Waves on a String simulation.

Since velocity is distance / time, we can apply the same idea to finding the . The distance a travels is its , and the time it takes to travel that distance is the . Combining these together we get two equations, one with and one with (remember T=1/f).

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.17-PDvzI4xRc3wh.png?alt=media&token=37bd96b7-656b-4eb8-bd4e-8e1437bcbc83

(or written like the Reference Table)

As long as the velocity of the remains constant (the material or tension doesn't change) we can see an inverse relationship between and . A lower means a larger and vice versa.

Sample Question (AP Classroom)

A travels to the right along a string.

a. Two dots have been painted on the string. In the diagrams below, those dots are labeled P and Q.

i. The figure below shows the string at an instant in time. At the instant shown, dot P has maximum displacement and dot Q has zero displacement from equilibrium. At each of the dots P and Q, draw an arrow indicating the direction of the of that dot. If either dot has zero velocity, write "v = 0" next to the dot.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.20-Zq8DDZTL9lhF.png?alt=media&token=69d73c1f-e93f-4b03-b2b6-ff3ba30d5d99

ii. The figure below shows the string at the same in stant as shown in part (a)i. At each of the dots P and Q, draw an arrow indicating the direction of the of that dot. If either dot has zero acceleration, write "a = 0" next to the dot.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.21-z30xJgb7KVZ9.png?alt=media&token=fd96d3db-05fc-41f4-a6cc-b1497e43a27d

b. The figure below represents the string at time t = 0 the same instant as shown in part (a) when dot P is at its maximum displacement from equilibrium. For simplicity, dot Q is not shown.

i. On the grid below, draw the string at a later time t = T/4, where T is the of the .

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.22-UJRMOsGndppi.png?alt=media&token=66abe122-9e25-487a-be13-790d26cd21ae

ii. On your drawing above, draw a dot to indicate the position of dot P on the string at time t = T/4 and clearly label the dot with the letter P.

c. Now consider the at time t = T. Determine the distance traveled (not the displacement) by dot P between times t = 0 and t = T.

Answer:

a) i.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.25-bVM4zNCL9Zcr.png?alt=media&token=b1b4a7f9-0235-4c8d-bc97-77f17cda05f3

At point P, the it at it’s lowest point so the point is not moving down or upwards at that time. At point Q, the particle is moving upwards to reach the top of the incoming crest in the next instant of time.

ii.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.26-hK5qID5Ck1Fv.png?alt=media&token=97c8aa94-20b2-4d69-b119-fcde6f2e6bf2

At point P, the particle is at the furthest distance from the equilibrium point which means that the force and acceleration on it must be at a maximum (very similar to mass on a spring from SHM Unit 6). Point Q is on the equilibrium point, so there is no net force or acceleration acting at that point.

b)i and ii.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.27-dxsALQZ6KYV7.png?alt=media&token=4665fd67-c481-464d-becd-ab45f2e8f681

Because the particle at point P must complete a full cycle of the in time T, time T/4 means that the particle must move ¼ of a cycle towards the right. So since the of the is 24cm, shift each part of the 6cm to the right. Point P was at 18cm in the previous diagram and doesn’t move with the (waves transfer and not mass) it will be in the same x location.

c) The particle at point P travels a complete cycle of the (from -8 to 8, then back to -8cm) for a total vertical distance of 32cm. It does not move horizontally at all.

🎥Watch: AP Physics 1 - Unit 10 Streams

Key Terms to Review (13)

Amplitude

: The amplitude represents the maximum displacement from equilibrium in a periodic motion.

Electromagnetic Waves

: Electromagnetic waves are a form of energy that can travel through space and matter. They consist of oscillating electric and magnetic fields that move perpendicular to each other.

Energy

: The ability to do work or cause change.

Frequency

: Frequency is the number of complete cycles or oscillations that occur in one second. It affects how many times an object vibrates back and forth within a given time period.

Instantaneous Acceleration

: Instantaneous acceleration refers to how quickly an object's velocity changes at a specific moment in time. It is calculated by finding the derivative of the object's velocity function with respect to time.

Instantaneous Velocity

: Instantaneous velocity refers to the speed and direction of an object at a specific moment in time. It is calculated by finding the derivative of the object's position function with respect to time.

Medium

: A medium refers to the substance or material through which a wave travels.

Momentum

: Momentum is a property of moving objects that depends on both their mass and velocity. It describes how difficult it is to stop an object in motion.

Period

: The period refers to the time it takes for one complete cycle of a repeating event or motion.

Transverse Wave

: A transverse wave is a type of wave in which the particles of the medium vibrate perpendicular to the direction of wave propagation.

Velocity of a Wave

: Velocity refers to how fast a wave travels through space or medium.

Wave

: A wave is a disturbance that transfers energy through a medium or empty space. It consists of oscillations or vibrations that move up and down or back and forth.

Wavelength

: The distance between two consecutive points on a wave that are in phase, such as from crest to crest or trough to trough.

10.1 Properties of Waves

6 min readjune 11, 2020

Peter Apps

Peter Apps

Peter Apps

Peter Apps

Enduring Understanding 6.A 👨‍💻

A is a travelling disturbance that transfers and .

Essential Knowledge 6.A.1 🏘

Waves can propagate via different oscillation modes such as transverse and longitudinal.

Essential Knowledge 6.A.2 🏘

For propagation, mechanical waves require a .

Essential Knowledge 6.A.3 🏘

The is the maximum displacement of a from its equilibrium value.

Essential Knowledge 6.A.4 🏘

Classically, the carried by a depends on and increases with . Examples include sound waves.

Anatomy of a

A is a periodic disturbance, meaning that it repeats over and over in a predictable pattern. The disturbance can cause the particles of the material the is propagating through to vibrate either perpendicular or parallel to the direction of the ’s motion.

If the particles vibrate parallel to the direction of motion, the is longitudinal. If they vibrate perpendicular, the is transverse.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.12-6uZnEgO7swdl.png?alt=media&token=65a14fda-3e5e-4d4c-a7f2-a49908b05ba3

Image courtesy of Difference.Wiki.

Both types of waves have similar features:

- The height of the , measured from the equilibrium position.

- The also describes the amount of a transfers. The higher the , the larger the .

- The distance from one repeated unit to the next.

- On a Longitudinal this is from compression to compression or rarefaction to rarefaction.

- On a this is from crest to crest, or trough to trough.

Other key terms that have been covered in Unit 6 include:

- the time it takes for one cycle of a to occur

- the number of cycles of a in a given amount of time

The depends on the (material) that the is traveling through. In AP 1, we only deal with mechanical waves that require a to travel through (they can’t travel through empty space which is a vacuum). If you go ahead and take AP 2, you’ll learn about that can travel through empty space. In general terms, mechanical waves travel faster through denser materials, or when the tension in the material is greater. You can mess around with this concept by taking a look at the PhET Waves on a String simulation.

Since velocity is distance / time, we can apply the same idea to finding the . The distance a travels is its , and the time it takes to travel that distance is the . Combining these together we get two equations, one with and one with (remember T=1/f).

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.17-PDvzI4xRc3wh.png?alt=media&token=37bd96b7-656b-4eb8-bd4e-8e1437bcbc83

(or written like the Reference Table)

As long as the velocity of the remains constant (the material or tension doesn't change) we can see an inverse relationship between and . A lower means a larger and vice versa.

Sample Question (AP Classroom)

A travels to the right along a string.

a. Two dots have been painted on the string. In the diagrams below, those dots are labeled P and Q.

i. The figure below shows the string at an instant in time. At the instant shown, dot P has maximum displacement and dot Q has zero displacement from equilibrium. At each of the dots P and Q, draw an arrow indicating the direction of the of that dot. If either dot has zero velocity, write "v = 0" next to the dot.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.20-Zq8DDZTL9lhF.png?alt=media&token=69d73c1f-e93f-4b03-b2b6-ff3ba30d5d99

ii. The figure below shows the string at the same in stant as shown in part (a)i. At each of the dots P and Q, draw an arrow indicating the direction of the of that dot. If either dot has zero acceleration, write "a = 0" next to the dot.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.21-z30xJgb7KVZ9.png?alt=media&token=fd96d3db-05fc-41f4-a6cc-b1497e43a27d

b. The figure below represents the string at time t = 0 the same instant as shown in part (a) when dot P is at its maximum displacement from equilibrium. For simplicity, dot Q is not shown.

i. On the grid below, draw the string at a later time t = T/4, where T is the of the .

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.22-UJRMOsGndppi.png?alt=media&token=66abe122-9e25-487a-be13-790d26cd21ae

ii. On your drawing above, draw a dot to indicate the position of dot P on the string at time t = T/4 and clearly label the dot with the letter P.

c. Now consider the at time t = T. Determine the distance traveled (not the displacement) by dot P between times t = 0 and t = T.

Answer:

a) i.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.25-bVM4zNCL9Zcr.png?alt=media&token=b1b4a7f9-0235-4c8d-bc97-77f17cda05f3

At point P, the it at it’s lowest point so the point is not moving down or upwards at that time. At point Q, the particle is moving upwards to reach the top of the incoming crest in the next instant of time.

ii.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.26-hK5qID5Ck1Fv.png?alt=media&token=97c8aa94-20b2-4d69-b119-fcde6f2e6bf2

At point P, the particle is at the furthest distance from the equilibrium point which means that the force and acceleration on it must be at a maximum (very similar to mass on a spring from SHM Unit 6). Point Q is on the equilibrium point, so there is no net force or acceleration acting at that point.

b)i and ii.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2FScreen%20Shot%202020-04-20%20at%208.27-dxsALQZ6KYV7.png?alt=media&token=4665fd67-c481-464d-becd-ab45f2e8f681

Because the particle at point P must complete a full cycle of the in time T, time T/4 means that the particle must move ¼ of a cycle towards the right. So since the of the is 24cm, shift each part of the 6cm to the right. Point P was at 18cm in the previous diagram and doesn’t move with the (waves transfer and not mass) it will be in the same x location.

c) The particle at point P travels a complete cycle of the (from -8 to 8, then back to -8cm) for a total vertical distance of 32cm. It does not move horizontally at all.

🎥Watch: AP Physics 1 - Unit 10 Streams

Key Terms to Review (13)

Amplitude

: The amplitude represents the maximum displacement from equilibrium in a periodic motion.

Electromagnetic Waves

: Electromagnetic waves are a form of energy that can travel through space and matter. They consist of oscillating electric and magnetic fields that move perpendicular to each other.

Energy

: The ability to do work or cause change.

Frequency

: Frequency is the number of complete cycles or oscillations that occur in one second. It affects how many times an object vibrates back and forth within a given time period.

Instantaneous Acceleration

: Instantaneous acceleration refers to how quickly an object's velocity changes at a specific moment in time. It is calculated by finding the derivative of the object's velocity function with respect to time.

Instantaneous Velocity

: Instantaneous velocity refers to the speed and direction of an object at a specific moment in time. It is calculated by finding the derivative of the object's position function with respect to time.

Medium

: A medium refers to the substance or material through which a wave travels.

Momentum

: Momentum is a property of moving objects that depends on both their mass and velocity. It describes how difficult it is to stop an object in motion.

Period

: The period refers to the time it takes for one complete cycle of a repeating event or motion.

Transverse Wave

: A transverse wave is a type of wave in which the particles of the medium vibrate perpendicular to the direction of wave propagation.

Velocity of a Wave

: Velocity refers to how fast a wave travels through space or medium.

Wave

: A wave is a disturbance that transfers energy through a medium or empty space. It consists of oscillations or vibrations that move up and down or back and forth.

Wavelength

: The distance between two consecutive points on a wave that are in phase, such as from crest to crest or trough to trough.


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.