TRANSVERSE PERIODIC WAVES

What happens when a mass vibrates up and down with a rope fastened to it?

A transverse periodic wave travels along the rope.

What does the wave consist of?

Crests and troughs.

What is the displacement of the crest in a wave?

Above its equilibrium position.

What is the displacement of the trough in a wave?

Below its equilibrium position.

What does every point on the rope execute ideally?

Simple harmonic motion with same amplitude and frequency.

How do wave crests and troughs travel?

They replace one another as the wave travels.

How do the rope points oscillate?

Up and down.

What is the amplitude of the wave?

Maximum value of displacement in crest or trough, equal to vibrator's amplitude.

What is wavelength in a periodic wave?

Distance between any two consecutive crests or troughs.

What symbol denotes wavelength?

Greek letter lambda.

How can wave speed be measured directly?

By timing the motion of a wave crest over a measured distance.

How can wave speed be found indirectly?

From frequency and wavelength.

What does Fig. 8.4 show?

Periodic wave moving to the right, snapshots every one-fourth of a time period.

How far does a crest move in one period?

One wavelength.

What is the formula for wave speed v?

v equals lambda divided by time period.

What does one divided by time period equal?

Frequency of the wave.

Final formula for wave speed using frequency?

v equals frequency times lambda.

What does the sine curve represent?

Periodic waves generated by simple harmonic motion.

What do points like C and C prime in Fig. 8.5 show?

They move in unison, in phase.

What does being 'in phase' mean?

Identical displacements and velocities.

How does C prime relate to C in phase?

C prime leads C by one time period or two pi radians.

What is the phase angle phi at a distance x?

Phi equals two pi times x divided by lambda.

What do points D and D prime show?

Points separated by whole multiples of lambda are in phase.

What is the condition for two points to be in phase?

Separated by lambda, two lambda, three lambda, and so on.

Can in-phase points be anywhere?

Yes, not just highest or lowest points.

What are examples of in-phase points besides crests or troughs?

Points like P, P prime, P double prime, and so on.

What’s the distance between any two in-phase points?

Lambda.

What are points called if they’re exactly out of step?

Out of phase.

What happens when C reaches max upward and D max downward at the same time?

C starts going down and D starts going up.

What are points separated by lambda over two, three lambda over two, five lambda over two called?

Out of phase.

Transverse periodic wave

A wave that travels along the rope with crests and troughs when one end is vibrated up and down.

Crest

Part of the wave where the rope is displaced above the equilibrium position.

Trough

Part of the wave where the rope is displaced below the equilibrium position.

Simple harmonic motion on rope

Every point on the rope executes simple harmonic motion with same amplitude and frequency.

Amplitude of wave

Maximum value of displacement in crest or trough, equal to amplitude of vibrator.

Wavelength (lambda)

Distance between any two consecutive crests or troughs.

Greek letter for wavelength

Lambda.

Measuring wave speed directly

By timing the motion of a wave crest over a measured distance.

Measuring wave speed indirectly

Using the wave’s frequency and wavelength.

Speed of wave formula

Speed equals lambda divided by time period.

Frequency (f)

Frequency equals one divided by time period.

Wave speed (frequency form)

Speed equals frequency times lambda.

Sine curve in wave motion

Graphical representation of periodic waves produced by simple harmonic motion.

In-phase points

Points with identical displacements and velocities, vibrating together.

Phase lead of one time period

Two pi radians.

Phase angle formula

Phase angle equals two pi times x divided by lambda.

Distance for in-phase points

Lambda, two lambda, three lambda, and so on.

In-phase locations

Any points on wave, not just crests or troughs, moving identically.

Out-of-phase points

Points exactly out of step, like crest versus trough at same instant.

Out-of-phase distance

Lambda over two, three lambda over two, five lambda over two, and so on.