Grandezze fondamentali delle onde en

AI-translated from Italian. Original page: Grandezze_fondamentali_delle_onde

Meaning of the symbols

symbol	meaning	SI unit
$c$	speed	m/s
$k$	wavenumber	1/m
$λ$	wavelength	m
$ν$	frequency	Hz
$T$	period	s
$ω$	angular frequency	rad/s

Relations between the fundamental quantities

	$c$	$k$	$λ$	$ν$	$T$	$ω$
$c$	=	$\frac{ω}{k}$	$λ ν$	$λ ν$	$\frac{λ}{T}$	$\frac{ω}{k}$
$k$	$\frac{ω}{c}$	=	$\frac{2 π}{λ}$	$\frac{2 π ν}{c}$	$\frac{2 π}{c T}$	$\frac{ω}{c}$
$λ$	$\frac{c}{ν}$	$\frac{2 π}{k}$	=	$\frac{c}{ν}$	$c T$	$\frac{2 π c}{ω}$
$ν$	$\frac{c}{λ}$	$\frac{c k}{2 π}$	$\frac{c}{λ}$	=	$\frac{1}{T}$	$\frac{ω}{2 π}$
$T$	$\frac{λ}{c}$	$\frac{2 π}{c k}$	$\frac{λ}{c}$	$\frac{1}{ν}$	=	$\frac{2 π}{ω}$
$ω$	$c k$	$c k$	$\frac{2 π c}{λ}$	$2 π ν$	$\frac{2 π}{T}$	=

The fundamental quantities listed in the previous section, which describe a wave, are not all independent of each other. The following table shows all the possible relations between them. Each quantity is defined and discussed on the pages how do we describe a wave? and properties of sound waves. Short definitions can also be found in the pages of the Glossary.

Check your understanding

Problem. A tuning fork emits A4 at 440 Hz in air, where sound travels at 343 m/s. Calculate the wavelength, period, angular frequency and wavenumber.

Solution. From the table:

λ = c / ν

= 343/440 m ≈ 0.78 m;

T = 1 / ν

≈ 0.00227 s = 2.27 ms;

ω = 2 π ν

≈ 2765 rad/s;

k = 2 π / λ = ω / c

≈ 8.06 rad/m.

Problem. The same tuning fork vibrates under water, where sound travels at 1480 m/s. Which quantities of the wave change and which do not?

Solution. The frequency (and therefore the period and the angular frequency) is set by the source and does not change: 440 Hz. What changes is the speed, the wavelength

λ = c / ν

= 1480/440 m ≈ 3.36 m and the wavenumber

k = ω / c

≈ 1.87 rad/m.

Problem. A wave is known to have wavenumber k = 2 rad/m and angular frequency ω = 680 rad/s. Find its speed, frequency and wavelength.

Solution.

c = ω / k

= 340 m/s;

ν = ω / 2 π

≈ 108 Hz;

λ = 2 π / k

≈ 3.14 m (and indeed

λ ν

≈ 340 m/s).

Physics, Waves, Music

Grandezze fondamentali delle onde en

From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.

Meaning of the symbols

Relations between the fundamental quantities

Check your understanding

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