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12.2 The Properties of Waves

GCSE Physics · AQA · Chapter 12: Wave Properties

A free GCSE Physics lesson for AQA (8463) from OBA School: amplitude, wavelength, frequency and period; the wave speed equation; measuring the speed of sound in air. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Define the amplitude, wavelength, frequency and period of a wave
  • Use period = 1 ÷ frequency, including unit prefixes such as kHz and ms
  • Use and rearrange wave speed = frequency × wavelength
  • Describe a method to measure the speed of sound in air

Key words

  • Amplitude: The maximum displacement of a point on a wave from its undisturbed (rest) position.
  • Wavelength, λ: The distance from a point on one wave to the same point on the next wave, e.g. crest to crest. Unit: metre (m).
  • Frequency, f: The number of waves passing a fixed point each second. Unit: hertz (Hz); 1 Hz = 1 wave per second.
  • Period, T: The time taken for one complete wave to pass a fixed point. Unit: second (s).
  • Wave speed, v: The distance a wave (and the energy it carries) travels each second. Unit: m/s.
  • Crest and trough: The highest point (peak) and the lowest point of a transverse wave.
  • Plane waves: Waves with straight wavefronts, such as those made by a straight bar in a ripple tank.

Describing a wave: amplitude and wavelength

A “snapshot” of a wave shows how far each point is displaced from its rest position at one instant. Two measurements describe its shape:

  • Amplitude is measured from the rest position to a crest (or to a trough). It is not crest to trough. A bigger amplitude means the wave carries more energy: louder sound, brighter light, bigger sea waves.
  • Wavelength λ (the Greek letter “lambda”) is the length of one complete wave, e.g. from one crest to the next, or from one trough to the next. For a longitudinal wave it is the distance from one compression to the next.

Exam tip: If a diagram shows a distance from crest to trough, halve it to get the amplitude. If it shows several waves, divide the total length by the number of complete waves to get λ.

Frequency and period

The frequency f is how many waves pass a point (or how many oscillations the source makes) every second. A guitar string vibrating 330 times each second makes a sound of frequency 330 Hz. Large frequencies use prefixes: 1 kHz = 1000 Hz, 1 MHz = 10⁶ Hz, 1 GHz = 10⁹ Hz.

The period T is the time for one complete wave. Frequency and period are linked:

period T (s) = 1 ÷ frequency f (Hz) and so f = 1 ÷ T

Worked example: period of a mains-hum sound

A transformer hums at 100 Hz. T = 1 ÷ f = 1 ÷ 100

Answer: T = 0.01 s (10 ms)

Worked example: frequency from a period

A buoy takes 2.5 s to bob up and down once. f = 1 ÷ T = 1 ÷ 2.5

Answer: f = 0.4 Hz

The wave speed equation

Imagine a source sending out f waves every second, each one λ long. In one second the front of the first wave has moved f × λ metres. So:

wave speed v (m/s) = frequency f (Hz) × wavelength λ (m)

Rearranged: f = v ÷ λ λ = v ÷ f

Also, for anything moving at a steady speed: speed (m/s) = distance (m) ÷ time (s)

Worked example: speed of waves on a lake

A jet ski makes waves with f = 0.50 Hz and λ = 7.0 m.
v = f λ = 0.50 × 7.0

Answer: v = 3.5 m/s

Worked example: wavelength of a radio wave (unit prefix)

A radio station broadcasts at 100 MHz = 100 × 10⁶ Hz = 1.0 × 10⁸ Hz. Radio waves travel at 3.0 × 10⁸ m/s.
λ = v ÷ f = 3.0 × 10⁸ ÷ 1.0 × 10⁸

Answer: λ = 3.0 m

Worked example: frequency of a sound

A sound has a wavelength of 85 cm = 0.85 m in air, where its speed is 340 m/s.
f = v ÷ λ = 340 ÷ 0.85

Answer: f = 400 Hz

In a ripple tank, if the bar vibrates faster, more waves are made each second and they are closer together: f goes up and λ goes down, but the speed stays the same. The speed of a wave depends on the medium (for water waves, on the depth); the frequency is set by the source.

Exam tip: Convert to base units first: kHz or MHz to Hz, cm or mm to m, ms to s. Then v comes out in m/s.

Measuring the speed of sound in air

Light travels so fast that you see an event almost instantly, but sound takes a noticeable time to cover a few hundred metres.

  • Two people stand at least 300–400 m apart on a field and measure the distance with a trundle wheel or tape.
  • One person bangs two blocks of wood (or cymbals) together above their head.
  • The other starts a stopwatch when they see the blocks hit and stops it when they hear the bang.
  • Repeat several times, ignore anomalous times, and find the mean time. Speed = distance ÷ mean time.

Worked example: processing results

Distance = 400 m. Times: 1.15 s, 1.22 s, 1.17 s. Mean = (1.15 + 1.22 + 1.17) ÷ 3 = 1.18 s
speed = 400 ÷ 1.18 = 339 m/s

Answer: about 340 m/s

The main error is human reaction time (about 0.2 s), which is large compared with a time of about 1 s. Using a larger distance makes the time longer, so reaction time causes a smaller percentage error. Swapping roles and averaging helps, and so does repeating. A better method uses two microphones a measured distance apart connected to a fast electronic timer, so no reaction time is involved.

Common mistakes

  • Measuring amplitude from crest to trough. Amplitude is from the rest position to a crest – half of the crest-to-trough height.
  • Forgetting to convert prefixes: 2 kHz is 2000 Hz and 25 cm is 0.25 m before using v = f λ.
  • Thinking a higher frequency makes a wave travel faster. In the same medium a higher frequency gives a shorter wavelength; the speed stays the same.
  • Mixing up period and frequency. Period is a time in seconds; frequency is a number per second in hertz.

Revision questions

Try these, then check your answers below each one.

Question 1. What is the amplitude of a wave? (Choose from: the maximum displacement of a point on the wave from its rest position, the distance from a crest to the next trough, the number of waves passing a point each second, the distance from one crest to the next crest.)

Answer: the maximum displacement of a point on the wave from its rest position

Working: Amplitude = maximum displacement from the rest (undisturbed) position, e.g. the height of a crest above the middle line.

Question 2. A wave has a frequency of 50 Hz. Calculate its period.

Answer: 0.02 s

Working: T = 1 ÷ f = 1 ÷ 50 = 0.02 s.

Question 3. The period of a sound wave is 4.0 ms. Calculate its frequency.

Answer: 250 Hz

Working: 4.0 ms = 0.0040 s; f = 1 ÷ 0.0040 = 250 Hz.

Related lessons

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This lesson is section 12.2 (AGCPH1202) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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