# Introduction and key concepts

 Page 1 / 1

## Introduction

We have already studied transverse pulses and waves. In this chapter we look at another type of wave called longitudinal waves. In transverse waves, the motion of the particles in the medium were perpendicular to the direction of the wave. In longitudinal waves, the particles in the medium move parallel (in the same direction as) to the motion of the wave. Examples of transverse waves are water waves or light waves. An example of a longitudinal wave is a sound wave.

## What is a longitudinal wave ?

Longitudinal waves
A longitudinal wave is a wave where the particles in the medium move parallel to the direction of propagation of the wave.

When we studied transverse waves we looked at two different motions: the motion of the particles of the medium and the motion of the wave itself. We will do the same for longitudinal waves.

The question is how do we construct such a wave?

To create a transverse wave, we flick the end of for example a rope up and down. The particles move up and down and return to their equilibrium position. The wave moves from left to right and will be displaced.

A longitudinal wave is seen best in a spring that is hung from a ceiling. Do the following investigation to find out more about longitudinal waves.

## Investigation : investigating longitudinal waves

1. Take a spring and hang it from the ceiling. Pull the free end of the spring and release it. Observe what happens.
2. In which direction does the disturbance move?
3. What happens when the disturbance reaches the ceiling?
4. Tie a ribbon to the middle of the spring. Watch carefully what happens to the ribbon when the free end of the spring is pulled and released. Describe the motion of the ribbon.

From the investigation you will have noticed that the disturbance moves parallel to the direction in which the spring was pulled. The spring was pulled down and the wave moved up and down. The ribbon in the investigation represents one particle in the medium. The particles in the medium move in the same direction as the wave. The ribbon moves from rest upwards, then back to its original position, then down and then back to its original position.

## Characteristics of longitudinal waves

As in the case of transverse waves the following properties can be defined for longitudinal waves: wavelength, amplitude, period, frequency and wave speed. However instead of peaks and troughs, longitudinal waves have compressions and rarefactions .

Compression
A compression is a region in a longitudinal wave where the particles are closest together.
Rarefaction
A rarefaction is a region in a longitudinal wave where the particles are furthest apart.

## Compression and rarefaction

As seen in [link] , there are regions where the medium is compressed and other regions where the medium is spread out in a longitudinal wave.

The region where the medium is compressed is known as a compression and the region where the medium is spread out is known as a rarefaction .

## Wavelength and amplitude

Wavelength
The wavelength in a longitudinal wave is the distance between two consecutive points that are in phase.

The wavelength in a longitudinal wave refers to the distance between two consecutive compressions or between two consecutive rarefactions.

Amplitude
The amplitude is the maximum displacement from equilibrium. For a longitudinal wave which is a pressure wave this would be the maximum increase (or decrease) in pressure from the equilibrium pressure that is cause when a peak (or trough) passes a point.

The amplitude is the distance from the equilibrium position of the medium to a compression or a rarefaction.

## Period and frequency

Period
The period of a wave is the time taken by the wave to move one wavelength.
Frequency
The frequency of a wave is the number of wavelengths per second.

The period of a longitudinal wave is the time taken by the wave to move one wavelength. As for transverse waves, the symbol $T$ is used to represent period and period is measured in seconds (s).

The frequency $f$ of a wave is the number of wavelengths per second. Using this definition and the fact that the period is the time taken for 1 wavelength, we can define:

$f=\frac{1}{T}$

or alternately,

$T=\frac{1}{f}$

## Speed of a longitudinal wave

The speed of a longitudinal wave is defined as:

$v=f·\lambda$

where

• $v=\mathrm{speed in m}·\mathrm{s}{}^{-1}$
• $f=\mathrm{frequency in Hz}$
• $\lambda =\mathrm{wavelength in m}$

The musical note “A” is a sound wave. The note has a frequency of 440 Hz and a wavelength of 0,784 m. Calculate the speed of the musical note.

1. $\begin{array}{ccc}\hfill f& =& 440\phantom{\rule{4pt}{0ex}}\mathrm{Hz}\hfill \\ \hfill \lambda & =& 0,784\phantom{\rule{4pt}{0ex}}\mathrm{m}\hfill \end{array}$

We need to calculate the speed of the musical note “A”.

2. We are given the frequency and wavelength of the note. We can therefore use:

$v=f·\lambda$
3. $\begin{array}{ccc}\hfill v& =& f·\lambda \hfill \\ & =& \left(440\phantom{\rule{0.277778em}{0ex}}\mathrm{Hz}\right)\left(0,784\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\right)\hfill \\ & =& 345\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\hfill \end{array}$
4. The musical note “A” travels at $345\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ .

A longitudinal wave travels into a medium in which its speed increases. How does this affect its... (write only increases, decreases, stays the same ).

1. period?
2. wavelength?
1. We need to determine how the period and wavelength of a longitudinal wave change when its speed increases.

2. We need to find the link between period, wavelength and wave speed.

3. 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 frequency is always unchanged, irrespective of any changes in speed. Since the period is the inverse of the frequency, the period remains the same.

4. The frequency remains unchanged. According to the wave equation

$v=f\lambda$

if $f$ remains the same and $v$ increases, then $\lambda$ , the wavelength, must also increase.

who are u?
Lamine
haha
Cleaford
scarm
nura
what it this
Cleaford
hi y'all
Dope
how does group chat help y'all 🤔
Dope
hi y'all
Dope
how does group chat help y'all 🤔
Dope
how does group chat help y'all 🤔
Dope
to learn from one another
Lamine
oh okay
Dope
😟
Creative
Yes
Lamine
what is type of economic
how to understand basics of economics
what is demand schedle
When you make a Scedule of the demand you made
Rodeen
What is macroeconomics
It's one of the two branches of Economics that deal with the aggregate economy.
Mayen
it's about inflation, occupation, gdp and so on
alberto
What is differences between Microeconomics and Macroeconomic?
Bethrand
a price floor of 24 imposed
monopolistic competition
yap
nura
any one there to answer my question
Fixed Costs per week Variable Costs per bear Rent & Rates of Factory Hire & machines Heating & Lighting Repayment of Bank Loan K100.00 K45.00 K5.00 K50.00 Materials Foam Wages K6.00 K1.00 K1.00 Total K200.00 K8.00
Richard
one of the scarce resources that constrain our behaviour is time. each of us has only 24 hours in a day. how do you go about allocating your time in a given day among completing alternatives? once you choose a most important use of time. why do you not spend all your time to it. use the notion of op
mohsina mala..Bangla app hobe na
mani Baba. First learn the spelling of Economics
Economics- The study of how people use their limited resources to tey and satisfy unlimited wants.
Kelly
hmmm
Mani
etar bangla apps hobe na?
Mohsina
what is defination of acnomics
বাংলা বই পাওয়া যায় না?
what is a commdity
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
Properties of longitudinal waves