Episode 311: Speed, frequency and wavelength

This episode considers how these three quantities are linked by the wave equation v = fλ , measuring f using an oscilloscope, and measuring the velocity of sound in free air.

Summary

  • Discussion and worked examples: Deducing and using the wave equation (30 minutes)
  • Student questions: Practice with v = f λ (30 minutes)
  • Demonstration: An exploration of sound waves (20 minutes)
  • Student experiment: Measuring frequency using a CRO (30 minutes)
  • Demonstration: Measuring the speed of sound using double beam oscilloscope (10 minutes)
  • Student experiments: Exploring waveforms (30–120 minutes)

Discussion and worked examples: Deducing and using the wave equation
Use a simple approach to deduce the wave equation

Justification/deduction of the wave equation v = f λ. For example: the coaches of a train are going past; you count how many coaches go by in a second and you know the length of one – so you multiply the two together to get the train’s speed. Apply this to waves: count the number of waves passing each second (= frequency), and multiply by the length of each (= wavelength) to find the speed.

Train

If your syllabus says deduce then you will have to present the algebra of

speed = distance/time = l/T= l / (1/f) = f λ.

Work through three examples:

A simple example, perhaps for sound in air, with values in Hz and m.

An example involving electromagnetic waves with frequency units such as MHz or GHz, to show how to deal with powers of ten; emphasise that c = 3 × 108 m s-1 for all em waves in free space.

An example in which the equation must be rearranged, to find f or λ.

Student questions: Practice with v = f λ.
You may wish to make a selection from these.

Episode 311-1: Speed, wavelength and frequency (Word, 47 KB)

Episode 311-2: Using the wave equation (Word, 42 KB)

Demonstration: An exploration of sound waves
An exploration of sound waves.

Turn the volume down each time you change the frequency range because of the differing sensitivity of the ear. Keep the overall volume low.

Emphasise that the oscilloscope trace represents displacement against time. You will have to hammer home that the peak-to-peak separation is not the wavelength.

It is advisable to perform this activity as a demonstration, as a room full of signal generators and loudspeakers in operation can be very noisy!

Safety
If you are going to use a stroboscope to show up the vibrations of a loudspeaker cone, you must check whether there is anyone in the class who may be affected by it. (You might wish to omit the use of the stroboscope.)

Episode 311-3: Exploring waveforms with an oscilloscope (Word, 49 KB)

Student experiment: Measuring frequency using a CRO
Students can measure the period, T, and hence calculate f. Each group will need a signal generator and a single beam oscilloscope.

Remind students to make sure that the oscilloscope is on the calibrated setting.

With a clear trace, note the time base setting and determine T (over several cycles if possible, an important technique). Then calculate f and compare with the setting on signal generator.

This is a good opportunity to check they are confident with the controls on the CRO and they can also explore the different waveforms from the signal generator.

(If you really have time for fun, issue low-voltage AC power supplies, switch off the timebase and input the 50 Hz signal to the X plates instead (often at the back) and give them the treat of Lissajous figures.)

Demonstration: Measuring the speed of sound using double beam oscilloscope
Connect two microphones to a double-beam oscilloscope. Set up a signal generator and loudspeaker to give sound waves of frequency 1 kHz. (Their wavelength is thus about 0.3 m.)

Place one microphone close to the loudspeaker, and observe its trace. Place the second microphone further from the loudspeaker, in the same straight line. Observe its trace. Move it back and forth, noting the changing phase difference between the two traces as you move through the sound waves.

Setup for measuring speed of sound

Measure the wavelength (with a ruler) by finding how far the microphone is moved between adjacent positions where the signals are in phase. Calculate the speed of sound.

Note that, if you don’t have two microphones, you can link the signal generator and loudspeaker to one input. Then find two consecutive positions of the microphone which are in antiphase with the signal. Antiphase is easy to see when the traces are superimposed on the screen.

If you don’t have a double beam oscilloscope, wait until a lesson on standing waves and then use a single beam one.

Student experiments: Exploring waveforms
These experiments make use of the CD-ROM ‘Multimedia Sound’. You could make a booklet from the relevant pages, so that students can investigate unsupervised in their own time.

Episode 311-4: Exploring waveforms with multimedia sound (Word, 37 KB)

Episode 311-5: Multimedia Sound: studying a pre-recorded sample (Word, 131 KB)

Episode 311-6: Multimedia Sound: recording your own sound sample (Word, 54 KB)

Episode 311-7: Superposition (Word, 63 KB)

Episode 311-8: Multimedia Sound: combining sounds (Word, 64 KB)

Download this episode
Episode 311: Speed, frequency and wavelength (Word, 446 KB)