Water waves and superposition

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Lesson notes

Water Waves

Water waves are formed in a **ripple tank** using a motor-driven **dipper** that vibrates up and down.
Each vibration of the dipper creates a water wave that travels outward.
Waves transfer **energy** without transferring **matter**.
Water waves are a type of **transverse wave**.

Transverse Waves

In a transverse wave, the vibration is **perpendicular** to the direction of wave travel.
For water waves, the dipper moves up and down while the wave moves outward horizontally.
Examples of transverse waves include water waves, light waves, and waves on a string.

Superposition

**Superposition** occurs when two waves pass through each other and overlap.
The **displacement** of a particle in a wave is its distance from the rest position.
During superposition, the displacements of the individual waves **add together**.

Constructive Interference

When two **peaks** (crests) arrive at the same place at the same time, they add together.
The amplitude of the combined wave is **greater** than each individual wave.
This is called **constructive interference**.

Destructive Interference

When a **peak** and a **trough** arrive at the same place at the same time, they cancel out.
The amplitude of the combined wave is **less** than each individual wave.
This is called **destructive interference**.

General Rule for Superposition

If displacements have the **same sign** (both positive or both negative), they add.
If displacements have **opposite signs**, they subtract.
The result is the **net displacement** at each point.

Constructive interference: two waves with same displacement sign add to produce a larger amplitude.

Destructive interference: a peak and trough cancel, resulting in zero displacement.

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Practice questions

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1.Which of the following is a transverse wave?
Easy
- AWater wave
- BSound wave
- CLongitudinal wave
- DP-wave
2.Water waves transfer energy without transferring what?
Easy
- AMatter
- BAmplitude
- CFrequency
- DWavelength
3.In a transverse wave, the vibration is ________ to the direction of wave travel.
Easy
- Aperpendicular
- Bparallel
- Copposite
- Dat 45°
4.What is superposition?
Easy
- AWhen two waves pass through each other and their displacements add
- BWhen a wave reflects off a barrier
- CWhen a wave changes speed
- DWhen a wave diffracts
5.When a peak of one wave meets a peak of another wave at the same place and time, what happens to the amplitude?
Medium
- AIt increases
- BIt decreases
- CIt stays the same
- DIt becomes zero
6.When a peak of one wave meets a trough of another wave at the same place and time, what happens to the amplitude?
Medium
- AIt decreases
- BIt increases
- CIt stays the same
- DIt doubles
7.In the ripple tank, what causes the water waves to form?
Medium
- AA motor connected to a dipper vibrating up and down
- BA fan blowing across the water surface
- CHeating the water
- DPouring water slowly
8.If two waves have displacements of +3 cm and -3 cm at the same point, what is the resultant displacement?
Medium
- A0 cm
- B6 cm
- C-6 cm
- D3 cm

More questions

9.Which statement about superposition is correct?
Hard
- ADisplacements of the same sign add, opposite signs subtract
- BDisplacements always add
- CDisplacements always cancel
- DDisplacements multiply
10.A student observes that when two water waves meet, the resulting wave has a smaller amplitude than either individual wave. What can be concluded?
Hard
- AA peak met a trough
- BTwo peaks met
- CThe waves were travelling in opposite directions
- DThe waves had different frequencies
11.If two identical waves with amplitude A undergo superposition where a peak meets a peak, what is the amplitude of the combined wave?
Hard
- A2A
- BA
- C0
- DA/2
12.In the ripple tank, the dipper moves up and down. In which direction do the water waves travel?
Hard
- APerpendicular to the dipper's motion
- BParallel to the dipper's motion
- COnly in the same direction as the dipper
- DIn a circular path
13.A ripple tank is set up with two dippers that produce identical water waves. The waves from the two dippers meet at a point where the displacement of one wave is +2 cm and the displacement of the other wave is +2 cm. What is the resultant displacement at that point?
Medium
- A0 cm
- B+2 cm
- C+4 cm
- D-4 cm
14.Two water waves travel towards each other. At a certain point, the displacement of one wave is -1.5 cm and the displacement of the other wave is +1.5 cm. What is the resultant displacement?
Medium
- A+3.0 cm
- B-3.0 cm
- C0 cm
- D+1.5 cm
15.A student observes that when two water waves meet, the resulting wave has a larger amplitude than either individual wave. Which of the following is the most likely explanation?
Hard
- AA peak meets a trough
- BA trough meets a trough
- CA peak meets a peak
- DThe waves are travelling in opposite directions
16.In a ripple tank, water waves are produced by a vibrating dipper. If the frequency of the dipper is increased, what happens to the wavelength of the water waves? (Assume the wave speed remains constant.)
Medium
- AWavelength increases
- BWavelength decreases
- CWavelength stays the same
- DWavelength becomes zero
17.A water wave has a frequency of 2 Hz and a wavelength of 0.5 m. What is the speed of the wave?
Hard
- A0.25 m/s
- B1.0 m/s
- C2.5 m/s
- D4.0 m/s
18.Two water waves of amplitude 3 cm each undergo superposition. At a point where a peak of one wave meets a trough of the other, what is the amplitude of the combined wave?
Medium
- A0 cm
- B3 cm
- C6 cm
- D9 cm
19.Which of the following is an example of a transverse wave?
Easy
- ASound wave
- BWater wave
- CLongitudinal wave
- DCompression wave
20.A student sets up a ripple tank and observes that water waves travel from the dipper to the edge of the tank. Which of the following is transferred by the waves?
Medium
- AMatter
- BEnergy
- CBoth matter and energy
- DNeither matter nor energy
21.Two water waves have displacements of +4 cm and -2 cm at the same point. What is the resultant displacement?
Hard
- A+2 cm
- B-2 cm
- C+6 cm
- D-6 cm
22.What is the name of the phenomenon that occurs when two waves pass through each other and their displacements add?
Medium
- AReflection
- BRefraction
- CSuperposition
- DDiffraction
23.In a ripple tank, the dipper moves up and down. In which direction do the water waves travel?
Medium
- AUp and down
- BOutwards in all directions
- COnly to the right
- DIn the same direction as the dipper
24.In a ripple tank, what is the purpose of the motor connected to the dipper?
Easy
- ATo make the dipper vibrate up and down
- BTo make the dipper move sideways
- CTo heat the water
- DTo change the colour of the waves
25.Which of the following statements about water waves is correct?
Easy
- AWater waves are transverse waves.
- BWater waves are longitudinal waves.
- CWater waves transfer matter.
- DWater waves do not transfer energy.
26.A ripple tank is set up with two dippers that produce identical water waves. At a point where a peak from one wave meets a peak from the other, what is observed?
Medium
- AThe amplitude increases.
- BThe amplitude decreases.
- CThe amplitude remains the same.
- DThe waves stop.
27.In a ripple tank, water waves are produced by a vibrating dipper. If the frequency of the dipper is increased, what happens to the wavelength of the water waves? (Assume wave speed remains constant.)
Medium
- AWavelength decreases.
- BWavelength increases.
- CWavelength stays the same.
- DWavelength becomes zero.
28.Two water waves of amplitude 4 cm and 2 cm undergo superposition at a point where the displacement of the first wave is +4 cm and the second is -2 cm. What is the resultant displacement?
Hard
- A+2 cm
- B+6 cm
- C-2 cm
- D+4 cm
29.A ripple tank experiment is set up with a single dipper. A student places a small cork on the water surface. As waves pass, the cork moves up and down but does not move horizontally towards the edge of the tank. What does this demonstrate?
Hard
- AWaves transfer energy without transferring matter.
- BWaves transfer matter without transferring energy.
- CThe cork is not affected by the waves.
- DThe cork is moving with the wave.
30.Two water waves of equal amplitude A undergo superposition. At a point where a peak of one wave meets a trough of the other, what is the amplitude of the combined wave?
Medium
- A0
- BA
- C2A
- DA/2
31.A water wave has a frequency of 5 Hz and a wavelength of 0.2 m. What is the speed of the wave?
Hard
- A1 m/s
- B5 m/s
- C0.04 m/s
- D25 m/s
32.A student observes that when two water waves meet, the resulting wave has a smaller amplitude than either individual wave. Which of the following is the most likely explanation?
Hard
- AA peak meets a trough.
- BTwo peaks meet.
- CTwo troughs meet.
- DThe waves are travelling in the same direction.
33.Which of the following statements about water waves is true?
Easy
- AWater waves are longitudinal waves.
- BWater waves transfer matter as they travel.
- CWater waves are transverse waves.
- DWater waves do not transfer energy.
34.In a transverse wave, the direction of vibration is ________ to the direction of wave travel.
Easy
- Aparallel
- Bperpendicular
- Cat 45°
- Dopposite
35.When two water waves meet and their displacements add together, this is called
Medium
- Areflection
- Brefraction
- Csuperposition
- Ddiffraction
36.Water waves transfer energy without transferring
Easy
- Aenergy
- Bmatter
- Cmomentum
- Dinformation
37.In a ripple tank, the dipper moves up and down. Which direction do the water waves travel?
Medium
- AUp and down only
- BIn the same direction as the dipper
- COutwards in every direction perpendicular to the dipper's motion
- DOnly in one direction away from the dipper
38.When a peak of one wave meets a trough of another wave at the same point, what happens to the amplitude of the combined wave?
Medium
- AIt becomes larger than either individual wave.
- BIt becomes smaller than either individual wave.
- CIt becomes zero if the amplitudes are equal.
- DIt remains unchanged.
39.Two identical water waves of amplitude 2 cm undergo superposition. At a point where a peak of one meets a trough of the other, what is the amplitude of the combined wave?
Hard
- A4 cm
- B2 cm
- C0 cm
- D1 cm
40.A water wave has a frequency of 3 Hz and a wavelength of 0.4 m. What is the speed of the wave?
Medium
- A0.133 m/s
- B1.2 m/s
- C7.5 m/s
- D3.4 m/s

Revision notes

## Water Waves and Superposition - Water waves are **transverse waves**: the vibration (up/down of dipper) is **perpendicular** to the direction of wave travel (outwards). - Waves transfer **energy** without transferring matter. - **Superposition** occurs when waves overlap; their **displacements add**. - **Constructive**: two peaks (or two troughs) meet → amplitudes add → larger amplitude. - **Destructive**: a peak meets a trough → amplitudes subtract (cancel) → smaller amplitude. - General rule: same sign displacements add; opposite signs subtract.

Transverse wave: A wave caused by a vibration that is perpendicular to the direction of wave travel.
Superposition: When two waves overlap, their displacements add together.
Constructive superposition: When two peaks (or two troughs) arrive at the same place at the same time, the amplitude of the combined wave is larger than each individual wave.
Destructive superposition: When a peak and a trough arrive at the same place at the same time, the amplitude of the combined wave is smaller than each individual wave.
Displacement: The distance a particle in the wave has moved from its rest position.

Flashcards

What do water waves transfer?

Water waves transfer energy without transferring matter.

What type of wave are water waves?

Water waves are transverse waves.

What causes a transverse wave?

A vibration that is perpendicular to the direction of wave travel.

In a ripple tank, what makes the dipper vibrate?

A motor connected to the dipper.

What happens each time the dipper vibrates in a ripple tank?

A water wave is formed.

What is superposition?

Superposition occurs when one wave passes through another, and their displacements add together.

What happens when two wave peaks arrive at the same place at the same time?

They add together, producing a combined wave with greater amplitude.

What happens when a peak and a trough arrive at the same place at the same time?

They cancel, producing a combined wave with smaller amplitude.

How do displacements add in superposition if they have the same sign?

They add together.

How do displacements add in superposition if they have opposite signs?

They subtract.

True or false: Water waves are longitudinal.

False.

True or false: Longitudinal waves are caused by a vibration perpendicular to wave travel.

False.

True or false: Water waves transfer energy without transferring matter.

True.

True or false: When two waves overlap, superposition occurs.

True.

Give one example of a transverse wave.

Water waves.

Describe how transverse waves are formed.

They are caused by a vibration that is perpendicular to the direction of wave travel.

What is the displacement of a wave?

The distance a particle in the wave has moved from its rest position.

In a ripple tank, which direction does the dipper move?

Up and down.

In a ripple tank, which direction do the water waves travel?

Perpendicularly in every direction outwards from the dipper.

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