Articoli sulla formula di definizione e sui tipi di onde meccaniche
DEFINIZIONE DI ONDE MECCANICHE
Se si tiene un'estremità di una corda e la si fa vibrare su e giù, si forma un'onda che si propaga lungo la corda. Oppure, se si lascia cadere un sasso nell'acqua, si formeranno delle onde sulla superficie dell'acqua. La corda e l'acqua oscillano solo verticalmente, non orizzontalmente. Le onde su una corda e le onde nell'acqua sono esempi di onde meccaniche.
Le onde meccaniche sono onde che si propagano attraverso un mezzo. Esempi di onde meccaniche sono le onde su corde o fili, le onde nell'acqua, le onde sonore che si propagano nell'aria e le onde sismiche che si propagano nel terreno. Le onde possono percorrere lunghe distanze finché il mezzo attraverso cui vibrano si trova in prossimità del punto di equilibrio.
TYPES OF MECHANICAL WAVES
Based on their shape, mechanical waves consist of two types, namely transverse waves, and longitudinal waves.
Transverse waves are waves that occur when the direction of the wave motion is perpendicular to the direction of the particle motion. For example, waves on a rope, waves on water.
If the waves in the string move in the horizontal direction, the particles in the string move in the vertical direction. Likewise, if water waves move in a horizontal direction, water particles move in a vertical direction.
Longitudinal waves are waves that occur when the direction of the wave motion is parallel to the direction of the particle motion. For example, waves in springs, and sound waves in air.
If the wave on the spring moves in a horizontal direction, then the density and strain that is formed in the spring also move back and forth in the horizontal direction.
Likewise, if the sound wave moves in the vertical direction, the air contracts and stretches in the vertical direction.
Earthquake waves consist of transverse waves (called shear waves) and longitudinal waves (called pressure waves).
MECHANICAL WAVE FORMULA
Transverse Wave Formula
Several quantities are used to describe waves, namely Amplitude (A), Frequency (f), Period (T), and Wave speed (v).
The amplitude is the maximum deviation. The period is the time interval of two successive wave crests/valleys that pass through the same point in space. Frequency is the number of peaks/valleys that pass the same point per unit of time.
Mechanical waves move at a certain speed. The wave speed formula is:
v = λ f = λ/T
v = wave speed, λ = wavelength, f = frequency, T = period.
The international unit for wavelength is meters, the unit for frequency is Hertz, and the unit for period is Seconds. The unit for wave velocity is meters/second.
Sample Problem:
A transverse wave on a string has a frequency of 2 Hz (2 wave crests pass through the same point in space, for 1 second) and has a wavelength of 3 meters (the distance between the two nearest crests is 2 meters). What is the wave speed?
Conosciuto:
Frequenza (f) = 2 Hz
Lunghezza d'onda (λ) = 3 metri
Ricercato: Velocità (v)
Soluzione:
v = λ f = 3 (2) = 6 m/s
The speed of a transverse wave in a medium depends on the nature of the medium through which it passes. For example, the wave speed on a string (rope, string, wire) depends on the tension in the string (FT) and the mass density of the string (the mass of the string per unit length).
Sample Problem:
A wave has a length of 1 meter and propagates on a string that is 100 meters long and has a mass of 2 kg. The tension in the rope is 200 N. What is the speed of the waves in the rope?
Conosciuto:
Wavelength (λ) = 1 meter
The length of the rope (L) = 100 meters
The mass of the rope (m) = 2 kg
The tension in the rope (T) = 200 N
Ricercato: Velocity of waves on a string (v)
Soluzione:
The Formula of the Longitudinal Wave
The speed of longitudinal waves in a medium depends on the nature of the medium through which it passes. The velocity of longitudinal waves that propagate on solid rods is calculated using the formula:
v = wave velocity, E = Young’s elastic modulus, ρ = density
Sample Problem:
Calculate the speed of the sound wave traveling along the steel rail. Young Steel’s modulus of elasticity = 2 x 1011 N / m2 and the density of steel = 7.8 x 103 kg / m3
Conosciuto:
The elastic modulus of Steel (E) = 2 x 1011 N / m2
Steel density (ρ) = 7.8 x 103 kg / m3
Ricercato: Speed of sound waves
Soluzione:
The speed of longitudinal waves that propagate in liquids and gases is calculated using the formula: v = wave velocity, B = bulk modulus, ρ = density
Sample Problem:
What is the speed of longitudinal waves when they travel through water?
Modulus of bulk water (B) = 2 x 109 N / m2
The density of water (ρ) = 1000 kg/m3
Soluzione:
Longitudinal wave speed when propagating in water:
