Transverse waves cause particles to vibrate perpendicularly to the direction of the wave's motion (e.g. waves on a string, ripples on a pond).

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1 Waves

2 Introduction A vibration must be the source of a wave. Waves in turn also cause vibrations. They are intrinsically connected. Waves transmit energy. There are different ways in which waves can be categorised. A wave is either a mechanical wave or it isn't. A mechanical wave is wave that requires a medium to propagate. A medium is space that contains some kind of uniform matter. For example water and air are different media, while vacuum is not considered to be a medium

3 Light, therefore is not a mechanical wave as it does not require a medium to propagate. A wave is either a longitudinal or transverse wave Longitudinal waves cause particles to vibrate parallel to the direction of motion of the wave (e.g. sound waves in all media) Transverse waves cause particles to vibrate perpendicularly to the direction of the wave's motion (e.g. waves on a string, ripples on a pond). Q: As mentioned vibrations are connected to waves. For light waves to be created what is intially vibrating?

4 The motion of particles in a wave can either be perpendicular to the wave direction (transverse) or parallel to it (longitudinal).

5 Sound waves are longitudinal waves:

can propagate through a fluid in the transverse direction, a fluid has no

6 Earthquakes produce both longitudinal and transverse waves. Both types can travel through solid material, but only longitudinal waves can propagate through a fluid in the transverse direction, a fluid has no restoring force. Surface waves are waves that travel along the boundary between two media.

7 Wave Motion A wave travels along its medium, but the individual particles just move up and down.

8 All types of traveling waves transport energy. Study of a single wave pulse shows that it is begun with a vibration and transmitted through internal forces in the medium. Continuous waves start with vibrations too. If the vibration is SHM, then the wave will be sinusoidal.

9 Wave characteristics: Amplitude, A Wavelength, λ Frequency f and period T Wave velocity υ

10 Example: If a wave has a time period of s, what is its frequency? Solution: f = 1 T = 1/0.25= 4.00 Hz

11 Example: Five full ocean waves pass by a fixed point in 20.0 s. What is the period and frequency of the wave? Solution: T = 20.0 s/5= 4.00 s f= 1/T= 5/20= 0.25 Hz

12 Example: A sound wave at standard atmospheric pressure and temperature has a speed of 344 m/s. What is the wavelength of a sound wave with a frequency of 256 Hz (middle C)? Solution: υ = f λ λ = υ f = 344/256= 1.34 m

13 Example: A speed of a transverse wave on a string depends on the tension and linear density of string: υ 2 = F T ρ l υ F T ρ l = velocity (m/s) = tension (N) = linear density (kg/m) If a wave along a string has a wavelength of 10.0 cm, and a frequency of 420 Hz, determine the linear density of the string? Assume the tension to be 25.0 N.

14 Solution: υ = f λ = (420)(0.1)= 42 m/s υ 2 = F T ρ l ρ l = F T υ 2 = 25/(42 2 )= 1.42x10-2 kg/m

15 Energy Transported by Waves Just as with the oscillation that starts it, the energy transported by a wave is proportional to the square of the amplitude. Definition of intensity: The intensity is also proportional to the square of the amplitude:

16 If a wave is able to spread out threedimensionally from its source, and the medium is uniform, the wave is spherical. Just from geometrical considerations, as long as the power output is constant, we see:

Reflection and Transmission of Waves A wave reaching the end of its medium, but where the medium is still free to move (smaller linear density), will be

17 Reflection and Transmission of Waves A wave reaching the end of its medium, but where the medium is still free to move (smaller linear density), will be reflected (b), and its reflection will be upright. A wave hitting an obstacle (larger linear density) will be reflected (a), and its reflection will be inverted.

18 At any boundary, there is a transmitted and reflected wave. A wave encountering a denser medium will be partly reflected (inverted) and partly transmitted; if the wave speed is less in the denser medium, the wavelength will be shorter.

19 Two- or three-dimensional waves can be represented by wave fronts, which are curves of surfaces where all the waves have the same phase. Lines perpendicular to the wave fronts are called rays; they point in the direction of propagation of the wave.

20 Interference; Principle of Superposition When two or more waves interact they interfere. Wave interference is governed by the principle of superposition. The superposition principle says that when two, or more waves pass through the same point, the displacement is the arithmetic sum of the individual displacements. In the figure below, (a) exhibits destructive interference and (b) exhibits constructive interference.

21 These figures show the sum of two waves. In (a) they add constructively; in (b) they add destructively; and in (c) they add partially destructively. Contructive interference Destructive interference

23 Standing Waves; Resonance Standing waves often called stationary waves are waves that don t appear to move. They are actually caused by the interference of waves moving and reflecting of the boundaries of the system. Any system has frequencies at which it would naturally resonate. These natural frequencies depend on the size and shape of the system and also the nature of the medium that makes up the system. The lowest possible frequency of vibration for a given system is call the fundamental frequency (first harmonic).

24 String fixed at both ends Standing waves occur when both ends of a string are fixed. In that case, only waves which are motionless at the ends of the string can persist. There are nodes, where the amplitude is always zero, and antinodes, where the amplitude varies from zero to the maximum value.

$Refraction If the wave enters a medium where the wave speed is different, it will be refracted its wave fronts and rays will change direction.$

25 Refraction If the wave enters a medium where the wave speed is different, it will be refracted its wave fronts and rays will change direction. We can calculate the angle of refraction, which depends on both wave speeds: Refraction will be examined more closely in the next section on light.

$The law of refraction works both ways a wave going from a slower$

26 The law of refraction works both ways a wave going from a slower medium to a faster one would follow the red line in the other direction.

$Diffraction When waves encounter an obstacle, they bend$

27 Diffraction When waves encounter an obstacle, they bend around it, leaving a shadow region. This is called diffraction.

$The amount of diffraction depends on the size of the obstacle compared to the wavelength.$

28 The amount of diffraction depends on the size of the obstacle compared to the wavelength. If the obstacle is much smaller than the wavelength, the wave is barely affected (a). If the object is comparable to, or larger than, the wavelength, diffraction is much more significant (b, c, d).

29 Sound

30 Characteristics of Sound Sound can travel through any kind of matter, but not through a vacuum. The speed of sound is different in different materials; in general, it is slowest in gases, faster in liquids, and fastest in solids. The speed depends somewhat on temperature, especially for gases.

31 Loudness: related to intensity of the sound wave Pitch: related to frequency. Audible range: about 20 Hz to 20,000 Hz; upper limit decreases with age Ultrasound: above 20,000 Hz; see ultrasonic camera focusing below Infrasound: below 20 Hz

32 Intensity of Sound: Decibels The intensity of a wave is the energy transported per unit time across a unit area. The human ear can detect sounds with an intensity as low as W/m 2 and as high as 1 W/m 2. Perceived loudness, however, is not proportional to the intensity.

33 The Ear and Its Response; Loudness

34 Outer ear: sound waves travel down the ear canal to the eardrum, which vibrates in response Middle ear: hammer, anvil, and stirrup transfer vibrations to inner ear Inner ear: cochlea transforms vibrational energy to electrical energy and sends signals to the brain

35 Interference of Sound Waves; Beats Sound waves interfere in the same way (principle of superposition) that other waves do in space. A beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies. f beat = f 1 f 2

36 Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow envelope around two waves that are relatively close in frequency.

37 Doppler Effect The Doppler effect occurs due to the relative motion of a source of sound and the observer.

38 As can be seen in the previous image, a source moving toward an observer has a higher frequency and shorter wavelength; the opposite is true when a source is moving away from an observer.

39 If the observer is moving with respect to the source, things are a bit different. The wavelength remains the same, but the wave speed is different for the observer. If the observer is moving towards the source it would have and effect of increasing the detected frequency, and if the observer were moving away from the source it would decrease the detected frequency. It is also possible to have a moving source and observer.

40 Shock Waves and the Sonic Boom If a source is moving faster than the wave speed in a medium, waves cannot keep up and a shock wave is formed. (12-)

41 Shock waves are analogous to the bow waves produced by a boat going faster than the wave speed of surface water waves.

42 Aircraft exceeding the speed of sound in air will produce two sonic booms, one from the front and one from the tail.

43 Another example of a similar wave phenomenon in light is Cherenkov radiation. This occurs when a charged particle travels through a medium faster than the speed of light can travel in this medium. (pic: blue glow in nuclear reactor)

44 Applications: Sonar, Ultrasound, and Medical Imaging Sonar is used to locate objects underwater by measuring the time it takes a sound pulse to reflect back to the receiver. Similar techniques can be used to learn about the internal structure of the Earth. Sonar usually uses ultrasound waves, as the shorter wavelengths are less likely to be diffracted by obstacles.

45 Ultrasound is also used for medical imaging. Repeated traces are made as the transducer is moved, and a complete picture is built.

46 Ordinary ultrasound gives a good picture; highresolution ultrasound is excellent.

Chapter 15 Wave Motion. Copyright 2009 Pearson Education, Inc.

Chapter 15 Wave Motion. Copyright 2009 Pearson Education, Inc. Chapter 15 Wave Motion 15-1 Characteristics of Wave Motion All types of traveling waves transport energy. Study of a single wave pulse shows that it is begun with a vibration and is transmitted through