13.1 Sound waves, seismic waves and graphs of motion

Graphs of particle position, displacement, velocity and acceleration

When a longitudinal wave moves through the medium, the particles in the medium only move back and forth relative to the direction of motion of the wave. We can see this in [link] which shows the motion of the particles in a medium as a longitudinal wave moves through the medium.

We can draw a graph of the particle's change in position from its starting point as a function of time. For the wave shown in [link] , we can draw the graph shown in [link] for particle 0. The graph for each of the other particles will be identical.

The graph of the particle's velocity as a function of 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 [link] is shown is [link] .

The graph of the particle's acceleration as a function of time is obtained by taking the gradient of the velocity vs. time graph. The graph of acceleration vs. time for the position vs. time graph shown in [link] is shown is [link] .

Sound waves

Sound waves coming from a tuning fork are caused by the vibrations of the tuning fork which push against the air particles in front of it. As the air particles are pushed together a compression is formed. The particles behind the compression 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 of the particles, there is a constant variation in the pressure in the air. Sound waves are therefore pressure waves. This means that in media where the particles are closer together, sound waves will travel quicker.

Sound waves travel faster through liquids, like water, than through the air because water is denser than air (the particles are closer together). Sound waves travel faster in solids than in liquids.

Sound will be studied in more detail in Chapter  [link] .

Seismic waves

Seismic waves are waves from vibrations in the Earth (core, mantle, oceans). Seismic waves also occur on other planets, for example the moon and can be natural (due to earthquakes, volcanic eruptions or meteor strikes) or man-made (due to explosions or anything that hits the earth hard). Seismic P-waves (P for pressure) are longitudinal waves which can travel through solid and liquid.

Summary - longitudinal waves

1. A longitudinal wave is a wave where the particles in the medium move parallel to the direction in which the wave is travelling.
2. Longitudinal waves consist of areas of higher pressure, where the particles in the medium are closest together (compressions) and areas of lower pressure, where the particles in the medium are furthest apart (rarefactions).
3. The wavelength of a longitudinal wave is the distance between two consecutive compressions, or two consecutive rarefactions.
4. The relationship between the period ( $T$ ) and frequency ( $f$ ) is given by
   $$T=\frac{1}{f}orf=\frac{1}{T}.$$
5. The relationship between wave speed ( $v$ ), frequency ( $f$ ) and wavelength ( $\lambda$ ) is given by
   $$v=f\lambda .$$
6. Graphs of position vs time, velocity vs time and acceleration vs time can be drawn and are summarised in figures
7. Sound waves are examples of longitudinal waves. The speed of sound depends on the medium, temperature and pressure. Sound waves travel faster in solids than in liquids, and faster in liquids than in gases. Sound waves also travel faster at higher temperatures and higher pressures.

Exercises - longitudinal waves

1. Which of the following is not a longitudinal wave?
   1. seismic P-wave
   2. light
   3. sound
   4. ultrasound
2. Which of the following media can sound not travel through?
   1. solid
   2. liquid
   3. gas
   4. vacuum
3. Select a word from Column B that best fits the description in Column A:

   Column A	Column B
   waves in the air caused by vibrations	longitudinal waves
   waves that move in one direction, but medium moves in another	frequency
   waves and medium that move in the same direction	white noise
   the distance between consecutive points of a wave which are in phase	amplitude
   how often a single wavelength goes by	sound waves
   half the difference between high points and low points of waves	standing waves
   the distance a wave covers per time interval	transverse waves
   the time taken for one wavelength to pass a point	wavelength
   	music
   	sounds
   	wave speed

4. A longitudinal wave has a crest to crest distance of 10 m. It takes the wave 5 s to pass a point.
   1. What is the wavelength of the longitudinal wave?
   2. What is the speed of the wave?
5. A flute produces a musical sound travelling at a speed of 320 m.s ${}^{-1}$ . The frequency of the note is 256 Hz. Calculate:
   1. the period of the note
   2. the wavelength of the note
6. A person shouts at a cliff and hears an echo from the cliff 1 s later. If the speed of sound is 344 m $·$ s ${}^{-1}$ , how far away is the cliff?
7. A wave travels from one medium to another and the speed of the wave decreases. What will the effect be on the ... (write only increases, decreases or remains the same )
   1. wavelength?
   2. period?