What is the Doppler effect? How does it apply to sound?

6 Pitch

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Pitch is the perception of sound, and is determined by frequency. It is thus the decibel equivalent [of intensity] for frequency. Higher pitches have higher frequencies, whereas lower pitches have lower frequencies. For example, comparing middle C with the G above, as G is a higher pitch, and has a higher frequency. Hearing range for humans is between 20 to 20,000 Hz, and this range declines with age.

“In high school, kids would put on that irritatingly high frequency sound that only kids can hear, and the teacher couldn’t,” Mandy said, “SO annoying!”

Remembering from that since velocity dependent on the medium’s physical properties, wave velocity will thus be constant in a given medium. Beatis interference between two sounds of slightly different frequencies [and therefore wavelengths], which causes total constructive interference at some point (demonstrated by increased amplitude, and since [mathjax]\propto A^2[/mathjax], therefore heard as increased intensity or loudness), and total destructive interference at some other point (demonstrated by, for vice versa reasons, softness), because of the differences in wavelengths. It sounds like periodic variations in volume, with a beat frequency equal to the difference between the two frequencies.

Piano tuners don’t just use the intuition of pitch to tune, but beats. Piano tuners play a note on the tuning fork and piano together, and hear for a beat. As stated , because the beat frequency is the difference between the two frequencies, the smaller the beat frequency, the closer the two notes. From since [mathjax]T=\dfrac{1}{f}[/mathjax], the less the beat frequency, the greater the beat period. Therefore, pianos cannot really be perfectly tuned, because a period of infinity would be required (i.e. wait forever).

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Maps to RK6.6

What is pitch?

7 Resonance

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Phase difference is important only when considered in relation to a reference plane, in particular, another wave. Interference is where two waves superimpose to form a resultant wave, determined by the superposition of the vertical displacements of the individual waves, which is addition of the constituent waves at every point. Where there is a phase difference of [mathjax]180^\circ[/mathjax]out of phase, note that there is total destructive interference, meaning that the vertical displacement is smaller at every point. Where the constituent waves are in phase, there is total constructive interference, meaning that the vertical displacement is greater at every point.

Note that in spite of medium change, for example, a thicker rope connected to a thinner rope, a wave in order to remain continuous (strings connected), must have the same frequency. Therefore, in medium change, frequency remains the same, and only wavelength and speed change. Additionally, there may be reflection and/or refraction. Reflection is the change in direction of a wave at an interface between different media, such that the wave returns into the medium from which it originated. Note that a wave reflecting off a string clamped on the opposing side, on the end of the string, will try to cause a force in the direction the amplitude is directed. However, because it is clamped down, it cannot occur. However, by Newton’s 3rd law, an equal but opposite force is created to the amplitude, thereby creating a wave pulse similar to the initial one, but with opposite polarity (upside down). In contrast, if it is not clamped down, the wave simply reflects with the same polarity. Analogously, if moving to a denser medium (similar to a hard boundary), the wave will be inverted ([mathjax]180^{circ}[/mathjax] out of phase). In contrast, if moving to a less dense medium, the wave will be upright (in phase). Refraction is the change in direction of a wave due to change in medium.

Standing waveis a wave that remains in a constant position. It is caused by two waves of the same frequency, wavelength and amplitude, travelling in opposite directions. The effect is a series of nodes (total destructive interference) and anti-nodes (total constructive interference) at fixed points along the line. Where the waves meet each other (in the middle) at [mathjax]\dfrac{\lambda}{2}[/mathjax], there is a node. Note that by definition, because the starting ([mathjax]0[/mathjax]) and ending points ([mathjax]n\lambda[/mathjax]) are fixed, they are also nodes. On either side of the middle, at [mathjax]\dfrac{\lambda}{4}[/mathjax] and [mathjax]\dfrac{3\lambda}{4}[/mathjax], there are anti-nodes.

Because the start and end points of a string are fixed and thus nodes, standing waves must be periodic at these nodes. Note there are essentially infinitely small division of waves that are periodic at the start and end nodes. The wavelength from the start and end node is the fundamental frequency, which is the lowest frequency [and since velocity is constant in any medium see [mathjax]f\propto \dfrac{1}{\lambda}[/mathjax], the longest wavelength]. The waves that are periodic at the fundamental frequency is known as resonance frequencies, which are frequencies that are an integer multiple of a fundamental frequency. So this would include 2f, 3f, 4f, etc.