Can someone tell me what is the frequency of the sound waves? Is it the number of compression or rarefaction going through in a second or the number of vibrations of the particles of the medium through which the sound travels per second? Are they the same thing? If so, how? I'm in 10th grade so please use simple language and less technical terms
Frequency – What is the Frequency of Sound?
acousticsfrequencywavelengthwaves
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Without using the terms resonance, harmonics etc you might explain it as follows.
Air blown through the lips with the aid of the edge of a hole at one end of the flute produces a series of pulses of higher than atmospheric pressure or compressions.
These compressions travel towards other open end of the flute.
Part of a compression escapes from the end but a part is reflected and travels back up the flute to the other end of the flute where again a part escapes and a part is reflected.
If the length of the flute is $L$ and the speed of the compression is $c$ it takes a compression a time $t = \frac {2L}{c}$ to travel from the hole by the lips, be reflected at the other end and then arrive back at the hole by the lips.
If at the same time when the compression arrives at the hole by the lips a new compression is being formed, the compression is magnified (there is a greater change in pressure).
If this process of magnification is repeated time and time again then that compression pulse and others like it produce a much larger amplitude series of compressions travelling towards the ear.
Compressions that do not take a time $t = \frac {2L}{c}$ to travel back and forth are not magnified indeed they may be destroyed if at the lip hole end an arriving compression meets a newly produced rarefaction (reduction in pressure).
Since it takes a time $t = \frac {2L}{c}$ for the compressions to travel up and down the tube this is also the time interval between compressions arriving at the ear.
The rate at which these compressions arrive is called the frequency $f = \frac 1 t = \frac{c}{2L}$ and so a note of frequency $f$ is heard. This note is called the fundamental.
Higher frequencies (harmonics) can be produced by, for example, producing a compression at the lip end when there is a compression just arriving at the other end. The frequency of this harmonic would then be twice that of the fundamental.
So a musical instrument has a source of pulses, a confined region along which the pulses can travel with only certain frequencies of pulses reinforcing one another.
Isn’t frequency how many cycles are completed per second, and isn’t the fundamental frequency only half a cycle
When a string, fixed a both ends, vibrates in the fundamental mode, the perpendicular displacement $\phi_1(x,t)$ of a point located at $x$ along the length of the string is given by
$$\phi_1(x,t) = A_1(t)\phi_1(x) = A_1\cos(2\pi f_1t + \varphi)\sin\left(\frac{\pi}{L}x\right)$$
Now, it is true that the spatial variation of the fundamental mode is a 'half-cycle' since the argument of the $\sin$ ranges from $0$ to $\pi$.
However, the fundamental frequency refers to the time dependent amplitude $A_1(t)$. Note that $A_1(t)$ executes $f_1$ cycles per second. Take a look at this animated gif of the fundamental mode and the first three harmonics:
See that although the fundamental mode has a 'half-cycle' spatial variation, the time dependent amplitude goes from a maximum, through zero, a minimum, back through zero back to the maximum in a time $T_1 = \frac{1}{f_1}$ where $f_1$ is the fundamental frequency.
Also note that the frequency of the 2nd harmonic is twice the frequency of the fundamental, the frequency of the 3rd harmonic is thrice the frequency of the fundamental and so on.
Best Answer
When sound travels through air, the frequency refers to the compression and rarefaction, not to a vibration of individual molecules.
The particles in the air are moving and colliding with each other at random. Typically an individual molecule might move at around 500 metres per second and collide several times per microsecond, so the motion is fast and chaotic. You can think of the motion due to sound to be a superimposed movement on top of the random movement of individual molecules, much as the current in a river is an overall movement quite distinct from the random motion of the individual water molecules.