Fourier Analysis of Sound Waves
Physics ⇒ Waves and Sound
Fourier Analysis of Sound Waves starts at 11 and continues till grade 12.
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See sample questions for grade 11
A complex sound wave is composed of frequencies 100 Hz, 200 Hz, and 300 Hz. What is the fundamental frequency?
A periodic sound wave has a period of 0.01 s. What is its fundamental frequency?
A sound wave is composed of the following harmonics: 200 Hz, 400 Hz, 600 Hz, and 800 Hz. What is the fundamental frequency?
A sound wave is described by the equation s(t) = 2sin(2π440t) + sin(2π880t). What are the frequencies present in the wave?
A sound wave is given by s(t) = 3sin(2π100t) + 2sin(2π200t). What is the amplitude of the second harmonic?
Describe the effect of removing higher harmonics from a complex sound wave.
Describe what is meant by the term 'frequency spectrum' in the context of sound waves.
Explain how Fourier analysis helps in identifying musical instruments from their sound.
Explain the difference between a pure tone and a complex tone in terms of Fourier analysis.
Explain why a clarinet and a flute playing the same note sound different, in terms of Fourier analysis.
Explain why Fourier analysis is important in digital music processing.
If a sound wave has a fundamental frequency of 200 Hz, what is the frequency of its third harmonic?
What is the main difference between the Fourier series and the Fourier transform?
What is the main purpose of using Fourier analysis in the study of sound waves?
A periodic sound wave has a fundamental frequency of 250 Hz. If its Fourier series contains only odd harmonics, what are the frequencies of the first three harmonics present?
A sound wave is composed of the following harmonics: 300 Hz, 600 Hz, 900 Hz, and 1200 Hz. If the amplitude of each harmonic is halved as the frequency increases, what is the amplitude of the 1200 Hz component if the 300 Hz component has amplitude 8 units?
A sound wave is represented by the function s(t) = 4sin(2π500t) + 2sin(2π1000t + π/2) + sin(2π1500t). Using Fourier analysis, identify the amplitude and phase of the second harmonic.
Describe how Fourier analysis can be used to distinguish between a tuning fork and a guitar string both playing the same note.
Explain how the phase of the harmonics in a Fourier series affects the shape of a sound wave, even if the amplitudes and frequencies remain unchanged.
