Aslevel Waves

Aslevels Physics Notes

Topic 7 : Waves

All vibrations produce wave of one type or another. A wave motion is a means of transferring energy from one point to another without there being any transfer of matter between the points. Waves that move through a material (or vacuum) are called progressive waves. A progressive wave transfers energy from one position to another. Waves may be classified as being either mechanical or electromagnetic.

Mechanical waves (e.g. water waves, sound waves, waves in stretched strings) require a material medium for their propagation

Electromagnetic waves (e.g. light coming from sun in the form of energy, radio, X-ray) can travel through a vacuum; their progress is impeded, to some extent, by the presence of matter.

When a mechanical wave travels from point A to some other point B, it is because a disturbance of some kind at A has caused the particle there to become displaced. This particle drags its neighbours with it, so that it too becomes displaced and has a similar effect on the next particle, and so on until the disturbance reaches B. if the material is elastic, the particles oscillate about their rest positions. The motions of any pair of particles are the same, but that of the particle which is farther from the source occurs somewhat later. If the disturbance at the source is of a repetitive nature, the wave is maintained. If it is not, the amplitude of vibration of each particle becomes progressively smaller and eventually the ceases to exist.

 There are two distinct types of mechanical waves, longitudinal and transverse.

• In longitudinal waves the particles of the medium vibrate parallel to the direction of the wave velocity. 
• In transverse waves, the particles of the medium vibrate at right angles to the direction of the wave velocity. 

Longitudinal waves are represented by sine curves (sinusoidal curves). The longitudinal wave shows how the material through which it is travelling is alternately compressed and expanded. This gives rise to high and low pressure regions, respectively. However this is rather difficult to draw, so longitudinal wave is also represented as if it were a sine wave. We can compare compression and rarefaction of the longitudinal wave with the crests and troughs of the transverse wave. 

Speed of a Wave

Whenever the source of a wave motion undergoes on cycle the wave moves forward by one wavelength λ. Since there are f such cycles each second, the wave progresses by 𝑓𝜆 in this time, and therefore the velocity (𝑣) of the wave is given by 𝑣 = 𝑓𝜆
It follows from the definition of period and frequency that 𝑓 = 1/t (One Divided by time in seconds)
The intensity of a wave is a measure of the energy passing through unit area per unit time. Since energy per unit time is power therefore intensity can be defined as power per unit area of cross-section. Intensity is measured in watt per square meter (Wm-² )

Doppler Effect

Whenever there is relative motion between a source of waves and an observer, the frequency of the wave motion as noted by the observer, is different from the actual frequency of the waves – this effect is known as Doppler Effect. The effect accounts for the sudden decrease in pitch (frequency) heard by a person standing in a railway station as a sounding train siren passes by.

When an emergency vehicle passes you while sounding its siren. The pitch is higher as it approaches you, and lower as it recedes into the distance. This is an example of the Doppler Effect.

Consider a source of sound waves of frequency,𝑓𝑠 , and wavelength, λ, and suppose that the speed of the waves is 𝑣. Let the source be at S at 𝑡 = 0 and suppose that it is moving along 𝑋𝑌 towards 𝑌 with velocity 𝑣𝑠 . Suppose that the source emits a crest when it is at 𝑆. The next crest will be emitted 1/𝑓𝑠  seconds later, by which time (remembering that 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × 𝑡𝑖𝑚𝑒) the first crest will have travelled a distance 𝑣 ( 1/𝑓𝑠 ) from 𝑆. That section of wavefront which is moving towards 𝑋 will have reached point 𝑀, and that which is travelling towards 𝑌 will have reached 𝑁. During his same time the source itself will have travelled a distance 𝑣𝑠 ( 1/𝑓𝑠 ), to T

Forward of the source

 

• The speed 𝑣 of the waves as they travel through the air (or other medium) is also unaffected by the movement of the source.

Electromagnetic spectrum

In 1864 James Clerk Maxwell used mathematical equations to describe how charges moving periodically in a conductor would set up alternating electric fields and magnetic fields in the nearby region. Maxwell knew that the magnetic and electric fields travelled through space. He calculated their speed and found 300 000 kms-¹ , exactly the same as the speed of light! Also, he devised mathematical expressions to describe the magnetic and electric fields. The solution to these expressions was found to be the equation of wave. Maxwell had shown that light is an electromagnetic wave.

Now we know that the electromagnetic spectrum includes a wide range of frequencies (or wavelengths). All electromagnetic waves are created by accelerating charges which result in a rapidly changing magnetic field and electric field travelling out from the source at the speed of light, electric and magnetic field components are at right angles to each other. Electromagnetic radiation meets the description of a transverse wave.

The many forms of EMR are essentially the same, differing only in their frequency and, therefore, their wavelength. The electromagnetic spectrum is roughly divided into seven categories depending on how the radiation is produced and the frequency. The energy carried by the electromagnetic radiation is proportional to the frequency. High-frequency short-wavelength gamma rays are at the high energy end of the spectrum. Low-frequency long-wavelength radio waves carry the least energy. Humans have cells in their eyes which can respond to EMR of frequencies between approximately 400 THz and 800 THz; these frequencies make up the visible light section of the electromagnetic spectrum.

The Doppler Effect with

The Doppler Effect occurs not only with sound but also with light.

When the light emitted by a star is examined spectroscopically, it is found that each line in the spectrum of any particular element is the star occurs at a different wavelength from that of the corresponding line in the spectrum of the same element in the laboratory. With some stars all the spectral lines are at longer wavelengths than in the laboratory spectrum; with others they are at shorter wavelengths. The shifts in wavelengths are interpreted as being due to the Doppler Effect. If the lines are at longer wavelengths (i.e. red shifted), the star is moving away from the Earth; if they are shorter wavelengths (i.e. violet shifted), the star is approaching us. The extent of the shift in wavelength depends on the speed with the star is moving relative to the Earth and can be used to calculate this speed. The Doppler Effect has also been used to measure the speed with which sun is rotating or the presence of double stars (double stars are two stars so close together that they appear as a single star even with a very large telescope).

The mathematical expression for Doppler Effect for light is similar to that of sound waves 

Where 𝑐 is the speed of light.