UNIT 1: mechanical waves / sound

Transcription

1 1. waves/intro 2. wave on a string 3. sound waves UNIT 1: mechanical waves / sound Chapter 16 in Cutnell, Johnson: Physics, 8th Edition Properties of waves, example of waves (sound. Light, seismic), Reflection, Doppler effect, shock wave, diffraction, refraction, Interference, resonance, standing waves, Physics of music, More on sound. Oscillation around an equilibrium position Oscillations can travel through medium such as water and air without carrying Matter along. These mechanic disturbances are called waves.

2 Part1 : Waves types and properties A wave is a traveling disturbance consisting of coordinate vibrations that transmit energy with not net movement of matter. The disturbance is frequently called an oscillation or vibration. The substance through which the wave travels is called the medium. The location of the energy is moving but there is no transfer of medium. A wave acts like a particle. 2

3 Imagine you are floating in the ocean and you are hit by Waves. You go up and down as waves pass you. It 10 waves pass you in 1 second that means 10 cycles per second. This is the frequency. The unit is Hertz. Since there are 10 cycles per second, this means each cycle (up,down,up) Lasts 1/10 = 0.1 second. This is the period. Unit is second. So period = 1/frequency As the waves pass you, you can measure the distance between 2 crests. This is the wavelength. The unit is meter. The maximum distance you reach Above the calm is is the amplitude. Unit is meter. The energy of the wave (a wave can do damage, break things) is proportional to the intensity 3 Which is proportional to the amplitude squared.

4 16.2 Periodic Waves In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position. The wavelength is the horizontal length of one cycle of the wave. The period is the time required for one complete cycle. The frequency is related to the period and has units of Hz, or s-1. 1 f = T

5 Waves types and properties- again The amplitude of a wave is the maximum displacement of the wave from the equilibrium position. It is just the distance equal to the height of a peak or the depth of a valley. 5

6 Waves types and properties, cont d The wavelength is the distance between successive like points on a wave. Like points might be peaks, valleys, etc. The wavelength is denoted by the Greek letter lambda: λ.

7 Compare the waves: Here is an illustration of changing the wavelength and/or amplitude. Lower amplitude implies smaller height/depth Shorter wavelength implies more complete waves fit in a given distance

8 Waves types and properties, cont d This figure illustrates the two main types of waves. Discuss

9 Waves types and properties, cont d There are two main wave types: Transverse waves have oscillations that are perpendicular (transverse) to the direction the wave travels. Examples include waves on a rope, electromagnetic waves, and some seismic waves. Longitudinal waves have oscillations that are along the direction the wave travels. Examples include sound and some seismic waves.

10 Waves types and properties, cont d We use different terminology for the peaks and valleys of a longitudinal wave. A compression is where the medium is squeezed together. A expansion is where the medium is spread apart.

11 Example of waves: sound waves Typically we represent a sound wave as a transverse wave (even though it is not). Sound wave = air pressure changes with time. A region of compression is drawn as a crest. A region of expansion is drawn as a trough. 11

12 16.5 The Nature of Sound Waves The distance between adjacent condensations is equal to the wavelength of the sound wave.

13 16.5 The Nature of Sound Waves Individual air molecules are not carried along with the wave.

14 Another example: Visible light is an electromagnetic wave. Light can travels in a vacuum. Each color is a given wavelength and a given frequency Frequency x wavelength = speed of light (186,000 miles/s in a vacuum) Light is an electric field and a magnetic field oscillating in the vacuum, the same Way sound wave is air pressure oscillating and seismic wave is stretching or Twisting of rocks. 14

15 Another example: Seismic wave traveling in Earth. 15

16 Waves types and properties, cont d The wavelength and frequency are related to the wave speed according to: v=λ f v is the wave s speed f is the wave s frequency λ is the wave s wavelength

17 Example Before a concert, musicians in an orchestra tune their instruments to the note A, which has a frequency of 440 Hz. What is the wavelength of this sound in air at room temperature? The speed of sound at this temperature is 344 m/s. 0.78m

18 You have waves in gas (sound) Wave in the vacuum (light) Wave in solid (Earthquake wave) Wave on liquid (water wave) Wave along 1 line (slinky, rope) Wave a long a surface 2D (ripples in water) Wave in 3D (sound) 18

19 A WAVE pulse A wave can be short and fleeting Like the burst of a balloon, a tsunami, Light from a camera. A wave can be continuous = train of pulses. Like the light from the Sun 19

20 Example The Wavelengths of Radio Waves AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x108m/s. A station broadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave. The atmosphere absorbs most of the wavelengths shorter than ultraviolet, most of the wavelengths between infrared and microwaves, and most of the longest radio waves. The radio window consists of frequencies which range from about 5 MHz (5 million hertz) to 30 GHz (30 billion hertz). The lowfrequency end of the window is limited by signals being reflected by the ionosphere back into space, while the upper limit is caused by absorption of the radio waves by water vapor and carbon dioxide in the atmosphere. As atmospheric conditons change the radio window can expand or shrink. On clear days with perfect conditions signals as high as 300GHz have been detected.

21 EXAMPLES Speed of a wave = distance / time = wavelength (m) / period(s) And period = 1/ frequency Frequency is the number of cycles per second And period is the time a cycle lasts in seconds. Source: The physics of every day phenomena. Griffith. Mc Graw Hill. 1. Suppose that water waves coming into a dock have a velocity of 1.2m/s and a wavelength Of 2.4m. With what frequency do these waves meet the dock? 2. Suppose the water waves have a wavelength of 1.4, and a period of 0.8s. What is the velocity of these waves? 3. A longitudinal wave on a slinky has a frequency of 5Hz and a speed of 2m/s. What is the wavelength of this wave? 4. A wave on a string has a speed of 12m/s and a period of 0.4s A)What is the frequency of the wave / B)What is the wavelength of the wave 5. A wave on a rope is shown below. Find the wavelength. If the frequency is 2Hz, what is the wave speed? 21 12m

22 Part2 : waves on a string Consider a string of length l and mass m. The speed at which a wave travels on the string when it is under a tension T is v= Τ. ρ ρ is the mass per unit length: ρ=mass of the string/length of the string more mass = more inertia = more resistance to motion. More tension = more force. See exploration of physics. See how speed depends on tension and on Inertia. See effect of fixed or free end.

23 Waves types and properties, cont d From this we see that the speed: Increases as the tension increases Is faster for smaller strings The string has a greater restoring force that attempts to straighten it out. The string has less mass that has to be moved by the restoring force. Is independent of the length The speed depends on the mass per length, not on just the length.

24 Example A student stretches a Slinky out on the floor to a length of 2 meters. The force needed to keep the Slinky stretched in measured and found to be 1.2 newtons. The Slinky s mass is 0.3 kilograms. What is the speed of any wave sent down the Slinky by the student? First step collect data: L=2m T=1.2N m= 0.3 kg Solve for V Density = mass/length in kg per m v= Τ. ρ

25 16.3 The Speed of a Wave on a String Example 2 Waves Traveling on Guitar Strings Transverse waves travel on each string of an electric guitar after the string is plucked. The length of each string between its two fixed ends is m, and the mass is g for the highest pitched E string and 3.32 g for the lowest pitched E string. Each string is under a tension of 226 N. Find the speeds of the waves on the two strings. CONVERT TO kg!!

26 16.3 The Speed of a Wave on a String High E v= F = m L ( 226 N = 826 m s kg ( m ) ) Low E v= F = m L 226 N = 207 m s -3 ( kg ) ( m )

27 Problems: 1. A certain rope has a length of 8m and a mass of 2.4kg. It is fixed at one end and held taut the other with a tension of 30N. The end of the Rope is moved up and down with a frequency of 2.5Hz. A. What is the mass per unit length of the rope? B)What is the speed of waves on this rope? C) What is the wavelength of waves on this rope having a frequency of 2.5Hz? D) How many complete cycles of these waves will fit on the rope? E) How long does it take for the leading edge of the waves to reach the other end Of the rope and start coming back? 2. Suppose that a guitar string has a length of 8.8m A mass of 0.12kg and a tension of 135N.. A. What is the mass per unit length of this string? B) What is the speed. Of a wave on this string? 3. A wave has a speed of 12m/s and a period of 0.4s. A0 What is the frequency of the wave? B) What is the wavelength of the wave?

28 PART 3: SOUND is a WAVE / speed of sound. Sound is a disturbance that travels at a speed of 340m/s At room Temperature. Or 1 mile in 5 seconds Or 1000 feet in 1 second. By comparison : Light covers 1 foot in s (10-9s)

29 We worked on the speed of a wave in a string. What about the speed of sound? The speed of sound in air = speed of molecules (they have a jiggling motion or random motion due to The temperature. They have kinetic energy ). Increase the temperature and the speed Increases too. (see applet exploration of physical sciences, 3 phases of matter) Temperature is a measure of their kinetic energy. T is proportional to mv2 (average kinetic energy of molecule). When T = absolute 0 = - 273C, the molecules Can't move anymore. Try to write a relationship between the speed of sound And the temperature. Brownian motion explained in 1905 by Einstein = the air molecules Have a random motion and kick a dust particle.

30 The speed of a sound wave when the air is at a temperature T is v = Τ. The temperature must be in Kelvin. T in kelvin = Celsius That's because the speed of sound = speed of the molecules make up the medium Carrying the sound. Temperature is a measure of the kinetic energy of the Molecules. So T is proportional to KE=0.5mv2 So v is proportional to the 30 Square root of T/

31 DISCUSSION: The factor of 20.1 depends on the properties of air. For other gases: Helium: v = Carbon dioxide: Τ. v = Τ. So why do your voice change when you inhale helium? (bad idea) 31

32 A little ( ) about temperature scales 32 To remember: a change in 2F (1.8 ) is about a change in 1C

33 Example What is the speed of sound in air at room temperature (20ºC = 68ºF)? Convert temperature to kelvin m/s or 1 mile in 5 seconds

34 The Speed of Sound in medium depend on the recoil force of molecules and their mass density. Like a wave on a rope, LIQUIDS SOLID BARS v= Bad ρ v= Y ρ Sound is faster in solid or liquid? Why train hijackers place their ears on rails?

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36 Assignments: v = v= Τ. ρ v=frequency x wavelength Τ. V is the speed of a sound wave Traveling in air at the temperature T. T is in kelvins = celsius +273 V is the speed of a mechanic wave traveling On a rope of linear density ϼ (m/s). The force T (N) was exerted on the rope by the source Of the wave. This is true for any kind of wave. Frequency is the number of cycles per seconds. Do the problems from next slide. Ref = inquiry to Physics SEE HINTS: - convert degrees to kelvin first million Hz = convert to Hz (1 million = 1,000,000 ) - Speed of sound in human tissue=1500m/s (about speed in water) - speed of water = 1500m/s - linear density = length /mass - convert cm to m (divide by 100) - MHz means 1,000,000 Hz

37 1.2 children stretch a jump rope between them and send wave pulses back and forth on it. The rope is 3m long. Its mass is 0.5kg, and the force exerted on it by the children is 40N. A) What is the linear mass density of the rope? B) What is the speed of the waves on the rope? 2. The force stretching the D string on a certain guitar is 150N. The string's linear mass density is 0.005kg/m What is the speed of waves on the string? 3. What is the speed of sound in air at the normal boiling temperature of water? 4. The coldest and hottest temperatures ever recorded in the united States are -83F (210K) and 135F (330K) respectively. What is the speed of sound in air at each temperature? 5. A 4Hz a continuous wave travels on a slinky. If the wavelength of 0.5m, What is the speed of waves on the slinky? 6. A 500Hz sound travels through pure oxygen. The wavelength of the sound is measured to be 0.65m. What is the speed Of sound in oxygen / 7. A wave traveling 80m/s has a wavelength of 3.2m. What is the frequency of the wave? 8. What frequency of sound traveling in air at 20C has a wavelength equal to 1.7m, the average height of a person? 9. What is the wavelength of 3.5 million Hz ultrasound as it travels through human body 10. The frequency of middle C on the piano is Hz A) What is the wavelength of sound with this frequency as it travels in air at room temperature B) What is the wavelength of sound with this frequency in water? A steel cable with total length 30m and mass 100kg is connected to 2 poles. The tension in the cable is 3,000N And the wind makes the cable vibrate with a frequency of 2Hz. Calculate the wavelength of the resulting Wave on the cable.

38 12. In a student laboratory exercise, the wavelength of a 40,000Hz ultrasound wave is measured to be 0.868cm Find the air temperature. 15. Ultrasound probes can resolve structural details with sizes approximately equal to the wavelength of the Ultrasound wave themselves. What is the size of the smallest feature observable in the human tissue examined With a 20MHz ultrasound, The speed of sound in human tissue is 1540m/s, 16. A sonic depth gauge is placed 5m above the ground. An ultrasound pulse sent downward reflects off snow and reaches the device 0.03 seconds after it was emitted. The air temperature is -20C. A0 How far is the surface of the snow from the device? B) How deep is the snow? DRAW TO GET IT. Not HARD. FROM INTRO physics BOOK. 17. The huge volcanic eruption on the island of Krakatoa, Indonesia, In 1883 was heard on Rodriguez Island, 4,782 km (2 970 miles) away. How long did it take the sound to travel to Rodriguez? 18. A baseball fan sitting in the : cheap seats is 150m from home plate. How much time elapses between the instant the fan sees a batter hit the ball and the moment the fan hears the sound? 19. A geologist is camped 8,000 m (5 miles) from a volcano as it erupts. A) How much time does it take the seismic waves produced by the eruption to reach the geologist's camp assuming the waves travel through granite as sound waves do? (google speed of sound in granite) 20. A sound emitted underwater reflects off a school of fish and is detected at the sameplace 0.01s later. How far away are the fish? (look for speed of sound in water) 38 Ref: Inquiry into Physics / Ostdiek and Bord Cengage Learning 2011