Spectrograms: tools to study wavesFrom Sun to Mud: Solar and Space Physics for the

Undergraduate Classroom !

Michael Hartinger

Source of Image: Prof. Donald Gurnett, University of Iowa

http://www-pw.physics.uiowa.edu/plasma-wave/istp/polar/gifs/13100_20.gif

Interpreting a Spectrogram

• Scientists use a tool called spectrograms to describe the intensity (or amplitude) and frequency of waves

• Spectrograms are often used to show wave intensity at different frequencies/times • What would the spectrogram for a tuning fork look like?

Time !

Freq

uenc

y !

Time !

Freq

uenc

y !

Grey/blue color = quiet or absence of sound wave

Red/white color = loud sound wave

Explain how sheet music tells you about the frequency and amplitude of sound waves: •Sheet music tells you whether to play a certain pitch/note (same concept as frequency) at a certain time. •When you play a note at the frequencies/times shown on the sheet music, you produce sound waves •If a scientist were to describe sheet music, they would say that the y-axis (vertical) part of each staff is for frequency, the x-axis (horizontal) for time, and the color is for intensity (black for finite sound wave intensity, white for zero intensity) !Explain the similarities between a spectrogram of piano music and sheet music: •The spectrogram on the bottom shows time on the x-axis, frequency on the y-axis, and sound wave intensity as color (red/white=intense sound wave, blue/grey=weak or no sound wave) •The general trends in the spectrogram on the bottom are the same as for the sheet music on the top – when the piano plays a higher note/frequency, the spectra shows more red/white near the top of the plot •Most musical instruments (even the piano) will have a complicated spectrum. In the above example, even though the piano player is only playing one or two keys/notes at a time, there are six or more peaks in the spectrum. Pianos, like other musical instruments, tend to make sound waves both at the desired note/frequencies as well as other frequencies (referred to as “harmonics”) – this is part of what makes the sound of different musical instruments so distinct/interesting. !Question: What would the spectrogram for a tuning fork look like? Answer: A tuning fork should produce as spectrogram with a single red/white flat line at one frequency (or perhaps several flat lines – tuning forks, although designed to produce only one frequency, will also produce sound at nearby frequencies [harmonics] – they are not perfect). See slide at end of presentation for more thorough answer. (To answer question correctly, students should understand that frequency is on the y-axis of a spectrogram, time on the x-axis, and wave intensity is color)

You can hear the grenades falling…

• During World War I, telephone operators picked up “whistlers”, a type of plasma wave named for the sound heard from telephone receivers (soldiers thought they sounded like grenades falling)

• Plasma waves don’t propagate in the Earth’s lower atmosphere, and humans can’t directly sense them

• These sounds came from electrical signals remotely induced in wires – the telephone speaker converted these currents to sound waves

Source: Robert Robinson, “Electronic Warfare in WWI”

It is important to remind students here that the telephone operators were not directly hearing plasma waves. Sound waves and plasma waves are two distinct phenomena, and humans can’t directly sense plasma waves:

•The frequency and amplitude of sound waves can be measured with a microphone. Or, it the sound is audible, with the human ear, which can discriminate frequency (often referred to as pitch in the context of music) and amplitude (loudness).

•The frequency and amplitude of plasma waves or electromagnetic waves can be measured with an antenna. Humans can’t sense plasma waves – however, some plasma waves can be heard if an antenna is used to pick up electrical signals associated with a plasma wave and a speaker is used to convert these signals to sound waves.

•WWI telephone operators were able to hear the sound waves from the telephone speaker because whistlers have frequencies in the human audible range (~20-20000 Hz) – not all plasma waves have frequencies in this range. !

Whistler waves

Source: Prof. Donald Gurnett, The University of Iowa

•A plasma is a gas that becomes so hot, electrons are stripped from atoms and the gas becomes “ionized” •It can support many unique types of wave disturbances, collectively known as plasma waves •We know now that the “whistlers” that WWI telephone operators heard are plasma waves that originate in the near Earth space environment •Whistlers have frequencies in the human audible range (~20-20,000 Hz)

*The spectrogram was generated using observations from the POLAR spacecraft, which has an antenna that measures the electric and magnetic fields associated with the plasma waves. These electric and magnetic fields are then processed and can be converted into audible sounds by a speaker (play the sound for the wave event shown in the spectrogram using the speaker icon) *A spectrogram is an essential tool for studying plasma waves, especially since we cannot hear or see the disturbances that plasma waves produce.

Frequency change

• Whistlers change their frequency over time, giving them a distinctive “bomb-dropping” sound

• Can you identify the whistler wave in this spectrogram? When does the whistler wave end? How much does the frequency change from time=14.0 seconds to end?

• If you converted the whistler to a sound wave via a speaker, could you hear it?

Source: spaceweather.com

Source of image: http://www.spaceweather.com/glossary/inspire.html !Question: Can you identify the whistler wave in this spectrogram? When does the whistler wave end? How much does the frequency change from time=14.0 seconds to end? Answer: The green line that gradually slopes downward. ~15.8 sec. ~-1300 Hz. (see slide at end of presentation for more thorough answer) (To answer question correctly, students should understand how to read off the frequency and intensity of wave activity from a spectrogram. They should not identify the flat horizontal or flat vertical lines in the spectrogram) !Question: If you converted the whistler to a sound wave via a speaker, could you hear it? Answer: Yes. The human audible range is ~20-20,000 Hz, and the frequency of the whistler lies within this range. (To answer question correctly, students should understand how to read off the frequency and intensity of wave activity from a spectrogram. They may need to be reminded that the human audible range is 20-20,000 Hz [shown on previous slide])

Ultra Low Frequencies

• The lowest frequency plasma waves in the near-Earth space environment are known as Ultra Low Frequency waves, or ULF waves

• In the spectrogram above, wave activity is recorded over a one hour period • Roughly, what is the frequency of the wave activity? If you used a speaker to

convert the plasma wave into a sound wave, could you hear it? • How fast would you have to play back the recording of this wave activity to hear it?

*Spectrograms can show very different time, frequency, and intensity ranges. Before comparing features on different spectrograms, it is important to first compare the ranges used for the axes on each spectrogram.

*For example, the time range on this spectrogram is 1 hour, whereas the time range for the spectrogram on the previous slide was a few seconds !Source of image: generated by Michael Hartinger using data from NASA’s THEMIS spacecraft !Question: Roughly, what is the frequency of the wave activity? If you used a speaker to convert the plasma wave into a sound wave, could you hear it? Answer: ~0.015 Hz. No, the human audible range is ~20-20,000 Hz, and the frequency of the ULF wave is outside this range. (To answer question correctly, students should understand how to read off the frequency and intensity of wave activity from a spectrogram. They may need to be reminded that the human audible range is 20-20,000 Hz) !Question: How fast would you have to play back the recording of this wave activity to hear it? Answer: 2.7 s, i.e., speed up the recording by a factor of ~1300. (see slide at end of presentation for more thorough answer) (To answer question correctly, students should understand that the time axis of a spectrogram can vary substantially for different wave events – i.e., they shouldn’t assume that two spectra that looks similar are showing the same type of wave activity. They may also need to be reminded that the lower end of the human audible range is ~20 Hz) !

References and Further Reading• On Plasma waves: • Sounds of the magnetosphere: http://www-pw.physics.uiowa.edu/plasma-

wave/istp/polar/magnetosound.html • An overview of different plasma waves (goes with the link above): http://

pwg.gsfc.nasa.gov/istp/polar/polar_pwi_descs.html • On overview of whistler waves and a few other types of plasma waves: http://

vlf.stanford.edu/research/introduction-vlf • An advanced overview of plasma waves: http://www-pw.physics.uiowa.edu/

plasma-wave/tutorial/waves.html • More on spectrograms of plasma waves: • http://www.spaceweather.com/glossary/inspire.html • • Program to convert sound files into spectrograms: • http://audacity.sourceforge.net/

• The following 3 slides contain answers to questions from presentation

Example of tuning fork spectrogram

• The tuning fork has a much steadier spectra (peaked at a single frequency/note) than piano music – a flat line at a single frequency

• In the example of a tuning fork spectra above there are harmonics which have lower intensities than the main frequency (but they are less pronounced than in the piano music) - tuning forks aren’t perfect.

Frequency change

• Whistlers change their frequency over time, giving them a distinctive “bomb-dropping” sound

• Can you identify the whistler wave that starts at time=13.6 seconds in this spectrogram? (circled in red) When does the whistler wave end? (~15.8 sec) How much does the frequency change from time=14.0 seconds to end? (-1300 Hz)

• If you converted the whistler to a sound wave via a speaker, could you hear it? (Yes – the range of frequencies audible to the human ear is ~20-20000 Hz)

The frequency changes from ~1600 Hz to ~300 Hz, ! Δf=-1300 Hz

Ultra Low Frequencies

• The lowest frequency plasma waves in the near-Earth space environment are known as Ultra Low Frequency waves, or ULF waves

• In the spectrogram above, wave activity is recorded over a one hour period • Roughly, what is the frequency of the wave activity? (0.015 Hz) If you used a speaker to convert the plasma wave into a

sound wave, could you hear it? (No, the lowest frequency humans can hear is roughly 20 Hz) • How fast would you have to play back the recording of this wave activity to hear it?

Frequency ≈ 0.015 Hz