Two points on a wave are half a wavelength apart. What is their phase difference?

180°. They are exactly out of step.

What does a progressive wave transfer from place to place?

energy. The medium only oscillates about its rest position.

What is the intensity of a wave?

power per unit area. It is measured in W/m².

Progressive waves · Cambridge A Level Physics 9702 revision

In plain words

A wave carries energy from one place to another while the stuff it travels through just oscillates on the spot. A handful of quantities describe any wave: how big, how long, how often, how fast, and how far out of step two points on it are.

4 things to know

Displacement is how far a point is from its rest position; amplitude is the maximum displacement. Wavelength λ is the distance between two neighbouring points that are in phase. Period T is the time for one oscillation, and frequency f = 1 ÷ T.
Wave speed v = fλ: in one period the wave moves forward by one wavelength.
Phase difference says how far out of step two points are, as a fraction of a cycle. One whole wavelength apart is 360° (2π radians); half a wavelength is 180°.
A progressive wave transfers energy. Intensity is the power per unit area: I = P ÷ A, in W/m².

Worked example

A sound wave travels at 340 m/s with a frequency of 500 Hz. Find the phase difference between two points 0.17 m apart.

Wavelength = v ÷ f = 340 ÷ 500 = 0.68 m.
0.17 m is 0.17 ÷ 0.68 = one quarter of a wavelength.
Phase difference = ¼ × 360° = 90° (π/2 radians).

Tips and tricks

On a displacement–distance graph you read off the wavelength; on a displacement–time graph you read off the period. Check the axis first.
Phase difference = (distance apart ÷ wavelength) × 360°.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Progressive waves: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What is the speed of a wave of frequency 200 Hz and wavelength 1.5 m?
- 133 m/s
- 201.5 m/s
- 300 m/s (the answer)
- 600 m/s
v = fλ.
Two points on a wave are half a wavelength apart. What is their phase difference?
- 90°
- 180° (the answer)
- 270°
- 360°
They are exactly out of step.
A wave has a frequency of 50 Hz. What is its period?
- 0.0020 s
- 0.020 s (the answer)
- 0.50 s
- 50 s
T = 1 ÷ f.
What does a progressive wave transfer from place to place?
- energy (the answer)
- matter
- energy and matter
- neither
The medium only oscillates about its rest position.
What is the intensity of a wave?
- power per unit area (the answer)
- energy per unit time
- force per unit area
- power × area
It is measured in W/m².

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.

Progressive waves

Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org

Name ______________________________ Date ______________

A wave has a period of 2.0 ms. Find its frequency.[2]
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500 Hz.
I got this one
Light with a power of 0.60 W falls evenly on a surface of area 0.030 m². Find the intensity.[2]
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20 W/m².
I got this one
A source radiates 100 W of sound evenly in all directions. Find the intensity 2.0 m from the source.[3]
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2.0 W/m². The power is spread over a sphere of area 4π × 2.0² = 50 m².
I got this one
Two points on a wave of wavelength 0.80 m are 0.20 m apart. Find their phase difference.[2]
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90° (π/2 radians). They are a quarter of a wavelength apart.
I got this one

Answers: Progressive waves

1. 500 Hz.
2. 20 W/m².
3. 2.0 W/m². The power is spread over a sphere of area 4π × 2.0² = 50 m².
4. 90° (π/2 radians). They are a quarter of a wavelength apart.