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The frequency spectrum. Objectives Investigate and interpret graphical representations of sound waves, including: o waveform graphs o frequency spectrum.

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Presentation on theme: "The frequency spectrum. Objectives Investigate and interpret graphical representations of sound waves, including: o waveform graphs o frequency spectrum."— Presentation transcript:

1 The frequency spectrum

2 Objectives Investigate and interpret graphical representations of sound waves, including: o waveform graphs o frequency spectrum graphs o spectrograms. Investigate and analyze characteristics of waves: frequency and amplitude.

3 1. G-sharp has a frequency of 417 Hz and the musical note A has a frequency of 440 Hz. If the two notes are graphed on the same waveform graph, how will the two curves differ? Assessment A.The A curve would be taller. B.The A curve would be shorter. C.The crests of the A curve would be closer together. D.The crests of the A curve would be farther apart.

4 2.One of these three graphs shows a sound that contains two different frequencies. a.Which graph is it and how do you know? b. What is the lower frequency in this sound? c. What is the higher frequency in the sound? Assessment

5 3.For which of the following would a spectrogram be able to represent different parts of sound? Assessment A.speech B.music C.bird songs D.all of the above

6 Assessment 4.At which frequency listed below is the sound represented on this spectrogram the loudest? A. 500 Hz B Hz C Hz D Hz

7 Physics terms microphone frequency spectrum Fourier’s theorem spectrogram

8 Sound waves are compression waves in air that cannot be seen. Several different kinds of graphs are used to help us visualize sound waves. Visualizing sound waves

9 A waveform graph describes how pressure changes over time. Notice the “zoomed-in” time scale. Waveform graphs This graph shows a single frequency of 417 Hz. (12.5 cycles in 0.03 seconds: the musical note G-sharp)

10 When multiple frequencies are present, the wave oscillates in a more complicated pattern. This waveform graph shows the addition of 300 Hz, 400 Hz and 450 Hz waves of the same amplitude. Waveform graphs

11 Real sounds contain thousands of different frequencies, all with different and changing phases and amplitudes. “Real” sound

12 A sound track is a waveform graph that displays complex sounds, such as music. Interpreting a sound track

13 A sound track is a waveform graph that displays complex sounds, such as music. The graph shows pressure as a function of time. To see individual oscillations, you have to zoom in on the time axis.

14 In Investigation 16C you will explore different graphical representations of sounds. Investigation Click on the simulation on page 453.

15 1.The simulation shows a waveform graph. Investigation: Part 1 Part 1: Multi-frequency sound Set a frequency of 300 Hz and adjust the volume. Set the time axis to display 0.02 s.

16 2.Add a 400 Hz and a 450 Hz sound. Listen to the frequencies separately and together and observe the wave form. Investigation: Part 1 Part 1: Multi-frequency sound Adjust the volume on ONE of the frequencies. Can you hear the changing frequency separately?

17 Investigation: Part 1 3.Switch the graph to display a spectrum—a bar chart that shows the frequencies of the sound. Set the same 3 frequencies as before and observe the spectrum as you change the frequency and volume. Part 1: Multi-frequency sound

18 4.Starting with 300 Hz, use three frequencies in the ratios 1:3:5 to create the best approximation to a square wave. Investigation: Part 1 Answer the questions in Part 1 of your student assignment. Part 1: Multi-frequency sound

19 Fourier’s theorem states that any repetitive wave can be reproduced exactly by combining simple sine waves of different frequencies and amplitudes. Fourier’s theorem provides a mathematical formula for determining this combination of waves, which is known as a Fourier series. Fourier’s theorem

20 How can this 100 Hz square wave be reproduced from a combination of sine waves? Fourier’s theorem: an example

21 The first four sine waves in the Fourier series (100 Hz, 300 Hz, 500 Hz, and 700 Hz) add up to a fairly good approximation. Adding more waves will make the approximation even better! How can this 100 Hz square wave be reproduced from a combination of sine waves? Fourier’s theorem: an example

22 This bar chart shows the relative amplitudes of the first four frequencies in the series. Spectrum of a square wave

23 Everyday sounds are more complicated than square waves. They contain thousands of different frequencies, each with its own amplitude and phase. This frequency spectrum is from an acoustic guitar playing the note E. Real spectra

24 The ear can listen to about 15,000 different frequencies simultaneously! Multi-frequency sound

25 The ear can listen to about 15,000 different frequencies simultaneously! The brain assembles a sonic “picture” from the changing patterns of rising and falling amplitudes at many thousands of frequencies. Multi-frequency sound

26 The waveform graph matches the in-and-out oscillation of your eardrum. This waveform graph shows pressure variations in the 3-frequency sound from the investigation.

27 Is it easy to deduce the original frequencies from the waveform? Multi-frequency sound The waveform graph matches the in-and-out oscillation of your eardrum. This waveform graph shows pressure variations in the 3-frequency sound from the investigation.

28 Is it easy to deduce the original frequencies from the waveform? Multi-frequency sound The waveform graph matches the in-and-out oscillation of your eardrum. No. The information is here, but it’s not easy to understand. There is another type of graph that lets you see frequency AND amplitude as a function of time.

29 1.Use the spectrogram tool to capture and display your voice. Investigation: Part 2 Modulate your voice and watch how the frequency and amplitude vary. Part 2: Real-time sound analysis

30 2.Repeat for various musical and non-musical sounds. Investigation: Part 2 Click the speaker symbols at the bottom of the investigation page to generate the various sounds shown here. Part 2: Real-time sound analysis

31 a.What characteristics make musical sounds different from other sounds? a.Describe how the spectrogram represents the three variables of time, frequency, and amplitude. Investigation: Part 2 Questions for Part 2

32 c.Interpret and compare the charts you generated for the frequencies in a voice to the frequencies you combined in Part 1. Are there more or fewer frequencies in the voice? d.Propose an explanation for how sound carries the information in words and music.. Investigation: Part 2 Questions for Part 2

33 A spectrogram depicts both frequency and loudness over time. Spectrogram charts Frequency is plotted vertically. Loudness is represented by color Time is plotted on the x-axis.

34 A spectrogram depicts both frequency and loudness over time. This spectrogram shows: 500 Hz tone that is soft, gets louder, and then soft again Spectrogram charts

35 A spectrogram depicts both frequency and loudness over time. This spectrogram shows: 500 Hz tone that is soft, gets louder, and then soft again soft 300 Hz tone (3 to 5 s) Spectrogram charts

36 A spectrogram depicts both frequency and loudness over time. This spectrogram shows: 500 Hz tone that is soft, gets louder, and then soft again soft 300 Hz tone (3 to 5 s) loud 200 Hz tone (1 to 3 s) Spectrogram charts

37 Interpreting spectrogram charts This spectrogram is of a human voice. How long does the sound last? Which is louder in this event, the low frequencies or the high frequencies? How do you know?

38 Interpreting spectrogram charts This spectrogram is of a human voice. How long does the sound last? about half a second. Which is louder in this event, the low frequencies or the high frequencies? How do you know? The low frequencies are red, indicating that they are louder. Can you infer from the graph if the speaker is a man or a young child?

39 This spectrogram is of a human voice. How long does the sound last? about half a second. Which is louder in this event, the low frequencies or the high frequencies? How do you know? The low frequencies are red, indicating that they are louder. Can you infer from the graph if the speaker is a man or a young child? This is a low male voice saying the word “hello”. Interpreting spectrogram charts

40 Digital sound recording As the spectrograms show, sound is highly complex and changes rapidly. How do sound engineers capture the sounds of music and voices? And how do we access these stored sounds to replay them later?

41 To record sound, a microphone converts pressure variations in the air into electrical signals. In CD-quality recording the signal is sampled 44,100 times a second by an analog to digital converter (ADC). Digital sound recording

42 The resulting string of numbers is recorded as data on a CD or other digital formats such as MP3. Digital sound recording

43 The electrical signal (a time-varying voltage) is amplified until it is strong enough to vibrate the coil in a speaker and reproduce the sound. Playback To play back the recording, the numbers are read by a laser and converted back into electrical signals by a digital to analog converter.

44 Assessment A.The A curve would be taller. B.The A curve would be shorter. C.The crests of the A curve would be closer together. D.The crests of the A curve would be farther apart. 1. G-sharp has a frequency of 417 Hz and the musical note A has a frequency of 440 Hz. If the two notes are graphed on the same waveform graph, how will the two curves differ?

45 Assessment A.The A curve would be taller. B.The A curve would be shorter. C.The crests of the A curve would be closer together. D.The crests of the A curve would be farther apart. 1. G-sharp has a frequency of 417 Hz and the musical note A has a frequency of 440 Hz. If the two notes are graphed on the same waveform graph, how will the two curves differ?

46 2.One of these three graphs shows a sound that contains two different frequencies. Assessment a.Which graph is it and how do you know? b. What is the lower frequency in this sound? c.What is the higher frequency in the sound?

47 2.One of these three graphs shows a sound that contains two different frequencies. Assessment a.Which graph is it and how do you know? Graph C is more complex. b. What is the lower frequency in this sound? 40 Hz c.What is the higher frequency in the sound? 80 Hz: It has two peaks for every one period of the lower frequency.

48 3.For which of the following would a spectrogram be able to represent different parts of sound? Assessment A. speech B. music C. bird songs D. all of the above

49 3.For which of the following would a spectrogram be able to represent different parts of sound? Assessment A. speech B. music C. bird songs D. all of the above

50 Assessment A. 500 Hz B Hz C Hz D Hz 4.At which frequency listed below is the sound represented on this spectrogram the loudest?

51 Assessment A. 500 Hz B Hz C Hz D Hz 4.At which frequency listed below is the sound represented on this spectrogram the loudest?


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