Describing a Wave | CAIE 9702 Paper 2 Notes

Paper 2

Physics9702

Describing a Wave

A few words describe any wave: displacement, amplitude, wavelength, period and frequency.

Learn each with its unit; the mark scheme is strict about them.

The five words to know

A wave frozen in space. Amplitude A is the height of a crest above the middle line; wavelength λ is the distance from one crest to the next.

Definition

1 mark

What is meant by amplitude?

Model answer: The maximum displacement from the equilibrium position.

Definition

1 mark

What is meant by wavelength?

Model answer: The shortest distance between two points on a wave that are in phase.

Displacement is the present signed distance from equilibrium. Amplitude is the largest magnitude of that displacement; it is not the crest-to-trough height.
Displacement, amplitude and wavelength are distances, so their SI unit is the metre.

Definition

1 mark

What is meant by period?

Model answer: The time taken for one complete oscillation.

Definition

1 mark

What is meant by frequency?

Model answer: The number of complete oscillations per unit time.

Period uses seconds. Frequency uses hertz, where 1 Hz means one complete oscillation each second.

f = \dfrac{1}{T}

Symbols

$f$ = frequency (Hz)
$T$ = period, the time for one cycle (s)

Frequency and period describe the same motion: a high frequency means a short period, and a low frequency means a long period.

Two graphs that look the same but are not

A displacement-distance graph is a snapshot of the whole wave frozen in space. Read the wavelength λ off it.
A displacement-time graph follows one point as time passes. Read the period T off it.

Two graphs that look identical. The left one is a snapshot along the wave (read the wavelength λ). The right one follows a single point over time (read the period T).

Common mistake

The two graphs look identical, so students read the wrong quantity. Check the horizontal axis first: if it says distance you get λ; if it says time you get T.

Worked example

Frequency from a period

A point on a wave takes 91 ms to complete one oscillation. Find the frequency.

One oscillation is one period, so $T = 91\text{ ms} = 0.091\text{ s}$ .
$f = \dfrac{1}{T} = \dfrac{1}{0.091} = 11\text{ Hz}$ .

Answer

f = 11\text{ Hz}

(9702/11/O/N/24 Q24)

Your turn9702/22/M/J/25 Q3(a)–(b)

A displacement-distance graph has a maximum displacement of 10.0 cm. Successive equal-phase points are 0.40 m apart. State the amplitude and wavelength. (9702/22/M/J/25 Q3(a)–(b))

Show worked answer

Answer

A=10.0\text{ cm},\quad\lambda=0.40\text{ m}

Describing a Wave

A few words describe any wave: displacement, amplitude, wavelength, period and frequency.

Learn each with its unit; the mark scheme is strict about them.

The five words to know

A wave frozen in space. Amplitude A is the height of a crest above the middle line; wavelength λ is the distance from one crest to the next.

Definition

1 mark

What is meant by amplitude?

Model answer: The maximum displacement from the equilibrium position.

Definition

1 mark

What is meant by wavelength?

Model answer: The shortest distance between two points on a wave that are in phase.

Displacement is the present signed distance from equilibrium. Amplitude is the largest magnitude of that displacement; it is not the crest-to-trough height.
Displacement, amplitude and wavelength are distances, so their SI unit is the metre.

Definition

1 mark

What is meant by period?

Model answer: The time taken for one complete oscillation.

Definition

1 mark

What is meant by frequency?

Model answer: The number of complete oscillations per unit time.

Period uses seconds. Frequency uses hertz, where 1 Hz means one complete oscillation each second.

f = \dfrac{1}{T}

Symbols

$f$ = frequency (Hz)
$T$ = period, the time for one cycle (s)

Frequency and period describe the same motion: a high frequency means a short period, and a low frequency means a long period.

Two graphs that look the same but are not

A displacement-distance graph is a snapshot of the whole wave frozen in space. Read the wavelength λ off it.
A displacement-time graph follows one point as time passes. Read the period T off it.

Two graphs that look identical. The left one is a snapshot along the wave (read the wavelength λ). The right one follows a single point over time (read the period T).

Common mistake

The two graphs look identical, so students read the wrong quantity. Check the horizontal axis first: if it says distance you get λ; if it says time you get T.

Worked example

Frequency from a period

A point on a wave takes 91 ms to complete one oscillation. Find the frequency.

One oscillation is one period, so $T = 91\text{ ms} = 0.091\text{ s}$ .
$f = \dfrac{1}{T} = \dfrac{1}{0.091} = 11\text{ Hz}$ .

Answer

f = 11\text{ Hz}

(9702/11/O/N/24 Q24)

Your turn9702/22/M/J/25 Q3(a)–(b)

A displacement-distance graph has a maximum displacement of 10.0 cm. Successive equal-phase points are 0.40 m apart. State the amplitude and wavelength. (9702/22/M/J/25 Q3(a)–(b))

Show worked answer

Answer

A=10.0\text{ cm},\quad\lambda=0.40\text{ m}