Everything Science Grade 11

14.4 CHAPTER 14. LONGITUDINAL WAVES

Step 1 : Determine what is required

We need to determine how the period and wavelength of a longitudinalwave

change when its speed increases.

Step 2 : Determine how to approach based on what isgiven

We need to find the linkbetween period, wavelength and wave speed.

Step 3 : Discuss how the periodchanges

We know that the frequency of a longitudinal wave is dependent on the

frequency of the vibrations that lead to the creation of the longitudinal wave.

Therefore, the frequencyis always unchanged, irrespective of any changes in

speed. Since the periodis the inverse of the frequency, the period remains the

same.

Step 4 : Discuss how the wavelength changes

The frequency remainsunchanged. According to the wave equation

v = fλ

if f remains the same and v increases, then λ, the wavelength, must also

increase.

14.4 Graphs of ParticlePosition, Displacement,Velocity and Acceleration

ESBGK

Tip

A particle in the medium
only moves back and
forth when a longitudi-
nal wave moves through
the medium.

When a longitudinal wave moves through the medium, the particles in the medium only move back

and forth relative to thedirection of motion of the wave. We can see thisin Figure 14.4 which shows

the motion of the particles in a medium as a longitudinal wave moves through the medium.

We can draw a graph ofthe particle’s change inposition from its startingpoint as a function of time.

For the wave shown in Figure 14.4, we can drawthe graph shown in Figure 14.5 for particle 0. The

graph for each of the other particles will be identical.

The graph of the particle’s velocity as a functionof time is obtained by taking the gradient of the

position vs. time graph.The graph of velocity vs. time for the position vs. time graph shown in

Figure 14.5 is shown isFigure 14.6.

The graph of the particle’s acceleration as a function of time is obtainedby taking the gradient of the

velocity vs. time graph.The graph of acceleration vs. time for the position vs. time graph shownin

Figure 14.5 is shown isFigure 14.7.

Tip

A sound wave is pro-
duced by an oscillating
object while a light wave
is not. Also, because
a sound wave is a me-
chanical wave (i.e. that
it needs a medium) it
is not capable of travel-
ling through a vacuum,
whereas a light wave can

travel through a vacuum. 14.5 Sound Waves ESBGL

Sound waves coming from a tuning fork are caused by the vibrations of the tuning fork which push

against the air particlesin front of it. As the air particles are pushed together a compression is formed.

The particles behind thecompression move further apart causing a rarefaction. As the particles

continue to push against each other, the sound wave travels through the air. Due to this motion ofthe

particles, there is a constant variation in the pressure in the air. Sound waves are therefore pressure

waves. This means thatin media where the particles are closer together,sound waves will travel

quicker.