1. ENGINEERING PHYSICS SEMESTER 2 2011/2012

2. ENGINEERING PHYSICS Introduction What is Vibration? A vibration can be defined as a back-and-forth motion around a point of rest or, more generally, as a variation of any physical property of a system around a reference value. Vibration refers to mechanical oscillations about an equilibrium point. The oscillations may be periodic such as the motion of a pendulum or random such as the movement of a tire on a gravel road. SEMESTER 2 2011/2012

3. ENGINEERING PHYSICS Types of Vibration Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. Examples: Pulling a child back on a swing and then letting go The mechanical system will then vibrate at one or more of its natural frequencies and damp down to zero. SEMESTER 2 2011/2012

4. ENGINEERING PHYSICS Types of Vibration Forced vibration is when an alternating force or motion is applied to a mechanical system. Examples: Shaking washing machining due to an imbalance, transportation vibration (caused by truck engine, springs, road, etc), or the vibration of a building during an earthquake. ● Magnitude of the vibration is strongly dependent on the behavior of the mechanical system SEMESTER 2 2011/2012

5. ENGINEERING PHYSICS Wave A wave is a disturbance that propagates through space or spacetime, transferring energy and momentum and sometimes angular momentum. OR A disturbance (interruption) traveling through a medium by which energy is transferred from one particle of the medium to another without causing any permanent displacement of the medium itself. SEMESTER 2 2011/2012

6. ENGINEERING PHYSICS Examples of Application of Waves SEMESTER 2 2011/2012

7. ENGINEERING PHYSICS Concept of Waves SEMESTER 2 2011/2012 The fundamental essence of a wave is the transfer of energy without the accompanying transfer of mass. In its most basic form, a wave is propagation of a disturbance through a medium. The medium is a collection of particles that exist at equilibrium positions – they are disturbed from these positions, they will feel a restoring force – thus, the particles are oscillators. In addition, these particles must interact with their neighbours, so that a disturbance can be passed from one particle to the next.

8. ENGINEERING PHYSICS Form of Waves SEMESTER 2 2011/2012 Transverse waves cause the medium to move perpendicular to the direction of the wave. Longitudinal waves cause the medium to move parallel to the direction of the wave. Surface waves are both transverse waves and longitudinal waves mixed in one medium. Example: water waves, sound waves, seismic waves.

9. ENGINEERING PHYSICS Types of Waves SEMESTER 2 2011/2012 Electromagnetic waves do not require a medium to travel (light, radio). Example: visible light, ultraviolet light, radio waves, television waves, microwaves, x-rays and radar waves Matter waves are produced by electrons and particles. Example: electrons, protons, atom, molecules. Mechanical waves require a material medium to travel (air, water, ropes).

10. ENGINEERING PHYSICS Waves Motion SEMESTER 2 2011/2012 A wave pulse is a disturbance that propagates through a medium. It transfers energy without transferring matter; the energy is a combination of kinetic and potential energy. Rythmic disturbance in both space and time is called wave, and the transfer of energy is said to take place by means of wave motion.

11. ENGINEERING PHYSICS Describing Waves SEMESTER 2 2011/2012 A harmonic disturbance can set up a sinusoidal wave. The distance from crest to crest, or trough to trough, is called the wavelength, λ. Amplitude (A): maximum displacement Wavelength ( λ): distance between points having the same phase Frequency (f ): number of waves passing per second Period (T ): time for one complete wave to pass

12. ENGINEERING PHYSICS SEMESTER 2 2011/2012 Relationship between wave speed (v), wavelength, period, and frequency: Waves may be either: a) Transverse (displacement perpendicular to direction of propagation) b) Longitudinal (displacement parallel to direction of propagation).

13. ENGINEERING PHYSICS Example SEMESTER 2 2011/2012 Figure above shows a sinusoidal wave traveling on a string at 240 m/s. Calculate: I)Amplitude of the wave, A ii)Wavelength, λ Iii)Frequency, f and Period, T

14. ENGINEERING PHYSICS Waves Properties: Superpositon and Interference SEMESTER 2 2011/2012 When two or more waves travel through the same medium at the same time, they interfere in a process called superposition. At any time/point, the combined waveform of two or more interfering waves is given by the sum of the displacements of the individual waves at each point in the medium.

15. ENGINEERING PHYSICS Example of Superpositon SEMESTER 2 2011/2012 At any time, the combined waveform of two or more interfering waves is given by the sum of the displacements of the individual waves at each point in the medium.

16. ENGINEERING PHYSICS Wave Properties SEMESTER 2 2011/2012 If the combined wave is larger than the individual ones, the interference is constructive; if smaller, it is destructive.

17. ENGINEERING PHYSICS Wave Properties SEMESTER 2 2011/2012 Destructive interference is used in noise- cancelling technology.

18. ENGINEERING PHYSICS Wave Properties: Reflection SEMESTER 2 2011/2012 Whether or not a wave is inverted upon reflection depends on whether the end is free to move or not.

19. ENGINEERING PHYSICS Wave Properties: Refraction SEMESTER 2 2011/2012 When a wave enters a new medium, its speed usually changes, as the properties of the new medium are different. The direction of propagation changes also; this is called refraction.

20. ENGINEERING PHYSICS Wave Properties: Refraction SEMESTER 2 2011/2012 If the speed of the wave depends on its wavelength, it exhibits dispersion. The rainbow of light from a prism is an example of dispersion. Diffraction – refers to the bending of waves around an edge of an object and is not related to refraction. Diffraction occurs when a wave passes through an opening that is comparable in size to the wavelength; the waves will “bend” around the edges of the opening.

21. ENGINEERING PHYSICS Standing Waves SEMESTER 2 2011/2012 On a rope with one fixed end, it is possible to set up waves that do not travel; they simply vibrate in place. These are called standing waves. Some points on the wave remain stationary all the time; these are called nodes. ● Others have the maximum displacement; these are called antinodes.

22. ENGINEERING PHYSICS Standing Waves and Resonance SEMESTER 2 2011/2012 Adjacent nodes are separated by half a wavelength, as are adjacent antinodes. When an integral number of half-wavelengths fit on the rope, the frequency is called the resonant frequency.

23. ENGINEERING PHYSICS Standing Waves and Resonance SEMESTER 2 2011/2012 Natural wavelengths,, can be varied by varying the length of a string, such as in a piano or harp; varying the mass per unit length, μ, of a string, as in a guitar; or varying the tension, which is done for fine tuning. Driving a system at its natural frequency produces resonance; the amplitude at resonance is limited only by damping and by the strength of the materials.

24. ENGINEERING PHYSICS Exercise SEMESTER 2 2011/2012 1. AM and FM radio waves are transverse waves that consists of electric and magnetic disturbances. These waves travel at a speed of 2.75 x m/s. A station broadcasts an AM radio wave whose frequency is 1500 x Hz (1500 kHz on the dial) and an FM radio wave whose frequency is 93.9 x Hz (93.9 MHz on the dial). Find the distance between adjacent crests in each wave. 2. A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.8 cm, a frequency of 51.2 Hz and a distance from a crest to the neighboring trough of 12.8 cm. Determine the period of such a wave.

25. ENGINEERING PHYSICS SEMESTER 2 2011/2012 3. Ocean waves are observed to travel along the water surface during a developing storm. A Coast Guard weather station observes that there is a vertical distance from high point to low point of 3.6 meters and a horizontal distance of 7.6 meters between adjacent crests. The waves splash into the station once every 5.3 seconds. Determine the frequency and the speed of these waves. 4. The string at the right is 6.0 meters long and is vibrating as the third harmonic. The string vibrates up and down with 45 complete vibrational cycles in 10 seconds. Determine the frequency, period, wavelength and speed for this wave.