TRANSVERSE & LONGITUDINAL WAVES

6.01

OBJECTIVES

• To understand the meaning of wave motion

• To distinguish between longitudinal and transverse waves

• To define amplitude, wavelength, period and frequency and state the relationship between them

• To understand the meaning of crest and trough

OBJECTIVES ( CONTD.)

• To find amplitude and period from a displacement- time graph

• To find amplitude and wavelength from a displacement- position graph

• To use v = λf

WAVE MOTION

How is wave motion different from the kind of motion you have studied so far?

WAVE MOTION

• Wave is a way of transferring energy from one place to another without the actual large scale motion of a material body.

• Light from the Sun warms up the earth

• A soprano singing can break a crystal glass

WAVE & DISTURBANCE

• A wave is always associated with a disturbance

DEFINITION OF WAVE

• A wave is a disturbance that transfers energy from one place to another

• The direction of energy transfer is the direction of propagation of the wave

MECHANICAL WAVES

• Require medium for propagation

• Sound waves, waves in a string, water waves are mechanical waves

ELECTROMAGNETIC WAVES

• Do not require medium for propagation

• Light is an electromagnetic wave

Wave & Particle Motion

• The wave, does exhibit a net displacement in space, whereas,

• the particles of the medium exhibit only

oscillatory motion around their equilibrium positions.

Longitudinal Waves

Longitudinal Waves

• Vibration direction parallel to wave propagation direction• Particles in medium move closer together/farther apart• Example: sound waves • Gases and liquids - support only longitudinal waves

Sound Waves

Sound waves are longitudinal waves, similar to the waves on a Slinky:

Here, the wave is a series of compressions and stretches.

Sound Waves

In a sound wave, the density and pressure of the air (or other medium carrying the sound) are the quantities that oscillate.

Transverse Waves

Transverse Waves

• Vibration direction perpendicular to wave propagation direction

• Example: plucked string

Solids - support both longitudinal and transverse waves

WATER WAVES

• What about water waves?

Water waves are a combination of transverse and longitudinal waves.

Wavelength

• The length of a full wave is called the wavelength, λ , and the time needed to produce one full wave is the time period T.

Speed of the Wave

• The wave moves forward a distance equal to a wavelength in a time equal to one time period

• The speed of the wave = distance / time• v = λ / T• Number of waves produced in one second=

frequency, f• f = 1 / T• v = λ f• ..\Desktop\PhET-1.0-windows-installer.exe

Graphical Representation of Waves

• Displacement- time graph

• Displacement – position graph

Parameters

• Distance : where along the wave are we looking

• Time: at what time are we looking at the wave

• Displacement : measures the disturbance

More on displacement

• String: the height of a point on the string from the undisturbed position of the string and is measured in units of length

• Sound: the change in the density of the medium relative to the equilibrium density and is measured in units of density

• Sound: the change in the pressure of the medium relative to the equilibrium pressure

Displacement

• All waves have a displacement

• The displacement is the difference of some quantity and the equilibrium value of that quantity when no wave is present

• The displacement of any waves is a function of position( distance) and time

Crest & Troughs

• Amplitude: the maximum displacement of the wave is called amplitude

• Crest: Points on the wave with maximum positive displacement are called crests

• Troughs: Points on the wave with maximum negative displacement are called troughs

Wavelength & Period from Graphs

• The distance between successive crests/ troughs in a displacement- distance graph is the wavelength

• The distance between successive crests/ troughs in a displacement – time graph is the time period.

Describing waves

PROBLEMS

• A sound wave of frequency 450Hz is emitted from A and travels towards B, a distance of 150m away. Take the speed of sound to be 341m/s.How many wavelengths fit in the distance from A to B?

Answer

• 198 wavelengths