# Definition formula and the types of mechanical waves

Articles about Definition formula and the types of mechanical waves

DEFINITION OF MECHANICAL WAVES

If you hold one end of the rope and vibrate it up and down, a wave appears that propagates along the rope. Or if you drop a stone into the water, waves will appear on the surface of the water. The rope and water only oscillate up and down, not moving horizontally. Waves on a rope and waves in water are examples of mechanical waves.

Mechanical waves are waves that travel through a medium. Examples of mechanical waves are waves on ropes or strings, waves in water, sound waves that propagate in the air medium, and earthquake waves that propagate in the soil medium. Waves can travel long distances while the medium through which the waves vibrate is around the equilibrium point.

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?

Known:

Frequency (f) = 2 Hz

Wavelength (λ) = 3 meters

Wanted: Speed (v)

Solution:

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?

Known:

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

Wanted: Velocity of waves on a string (v)

Solution:

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

Known:

The elastic modulus of Steel (E) = 2 x 1011 N/m2

Steel density (ρ) = 7.8 x 103 kg/m3

Wanted: Speed of sound waves

Solution:

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

Solution:

Longitudinal wave speed when propagating in water: