3. What is Sound? Recall from the speaker lab and intro waves notes that a sound wave (pressure wave) is a longitudinal wave. A disturbance is created in a medium creating a change in pressure. The particles of the medium (air or water) are temporarily displaced and then return to their original position. DEMO: A cell phone in a “vacuum” produces ____ sound! NO

4. We represent a longitudinal sound wave as a transverse sine wave… Like all waves, sound waves, then, have an amplitude, a wavelength, a frequency, and a speed… Amplitude of a sound wave relates to the ________ of the sound. loudness

5. What we hear Assuming a high enough amplitude the audible range for humans is about 20 – 20,000 Hz. Below 20 Hz = ___________ and above 20,000Hz = ___________ So is the amplitude the reason why humans can’t hear a dog whistle? _____! The frequency of the dog whistle is higher than what our ear drums can perceive. Dogs can detect frequencies as low as approximately 50 Hz and as high as 45,000 Hz. WOW! NO Ultrasonic Subsonic f = 1/T

6. Pitch The sensations of the frequencies we hear are commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency and a low pitch sound corresponds to a low frequency. When two sounds with a frequency difference of 7 -15 Hz are played simultaneously, most people are capable of detecting the presence of a complex wave pattern resulting from the interference and superposition of the two sound waves. Any two sounds whose frequencies make a 2:1 ratio are said to be separated by an octave and when played together are sound pleasing to most people.

7. The Speed of sound does NOT have 1 set value. It depends on the ________ through which the sound wave is traveling. The speed of sound in air depends on the air temperature, T, according to…. The speed of sound at “standard temperature” is approximately… Use this value if no temp. is given Why?? As T , molecules move quicker, so less time to “bump” into a neighboring molecule to transmit the vibration. medium

8. The speed of sound is ≈ ____ faster in water than air. The speed of sound is ≈ ____ faster in steel than air. A question that puts it all together: If the pitch of a sound is decreased, the frequency ___ the wavelength ___ the wave speed (or velocity) ___ the amplitude ____ Recall 4 x 11 x ↓ ↑ stays same

9. The Doppler Effect The Doppler effect, named after Christian Doppler, is the change in frequency and wavelength of a wave as perceived by an observer moving relative to the source of the waves. Johann Christian Andreas Doppler (1803- 1853) was an Austrian mathematician and physicist, who first proposed the effect in 1842. He noticed that an approaching train's whistle has a high pitch. As it passes by, however, the sound of the train whistle suddenly becomes much lower. We have all experienced his discovery.

10. A stationary sound source… A stationary sound source to the left produces sound waves at a constant frequency and the wavefronts propagate symmetrically away from the source at a constant speed, which is the speed of sound in the medium. The distance between wavefronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source. Doppler animations courtesy of Dan Russell – Kettering University

11. A moving sound source… The same sound source is radiating sound waves at a constant frequency in the same medium. Now the sound source is moving to the right. The wavefronts are produced with the same frequency as before, but since the source is moving, the center of each new wavefront is now slightly displaced to the right. Therefore, the wavefronts begin to bunch up in front and spread further behind the source. speed v s = 0.7 v (Mach 0.7).

12. What do we hear? An observer on the right (in front of the moving truck) would hear sound waves that have a _________ wavelength and, thus, a _________ frequency (pitch). At the same time, an observer on the left (behind themoving truck) would hear sound waves that have a ________ wavelength, and, thus, a ______ frequency. shorter higher longer lower

13. Of course there MUST be a way to calculate these changes in frequency… YAY MATH!! We will derive a formula to calculate the frequency that is heard by a stationary observer if a horn is moving toward the observer… We’ll let f and be the actual frequency and wavelength of the horn and v is the speed of the sound waves (as always). The speed of the horn (the source) we will call V s. For one period, T, then, the horn has moved… d = _____ = _____ (recall ) λ

14. So the observed wavelength will be _____ than the actual wavelength,, by this amount, d… The observed frequency,, can be found using since the speed of sound, v, is constant. Solve for by multiplying both sides by the reciprocal This will work for the frequency heard by a stationary observer with the source moving towards him… less

15. However, there are lots of other cases to consider, such as if the source is moving away, or if the observer is moving towards the source, just to name a few. Without deriving each case, the general formula is… Where… f’ = frequency heard by receiver f = actual frequency of source v r = speed of receiver v s = speed of source v = speed of sound (340 m/s)

16. So how do we use this equation? How do we know whether to choose + or -? …. Just THINK! Ask yourself these questions: 1.Is the source moving toward or away from the receiver? Say it’s towards… So… should the frequency be higher or lower? In this case…. _________. Now, what do I need to do to the denominator to make it higher or lower? In this case, make it higher by making the denominator ________  Use ____________ higher smaller subtraction

17. 2.Is the receiver moving toward or away from the source? Say it’s away… So… should the frequency be higher or lower? In this case….__________. What do I need to do to the numerator to make it higher or lower? In this case, make it lower by making the numerator ________.  Use ____________. lower smaller subtraction Doppler effect Video Doppler Sound Clip

18. Doppler examples: 1. You are standing on a platform waiting for a train. As the train approaches the station, it gradually slows down. During this process of slowing down, the engineer sounds the horn at a constant frequency of 300 Hz. What pitch or changes in pitch will you perceive as the train approaches you on the loading platform? A.This is a tough question! First you know that the pitch which you hear will be greater than 300 Hz since the sound source is approaching you. But once stopped, the pitch will be 300 Hz exactly. So the pitch must be gradually decreasing from above 300 Hz to 300 Hz during the slowing down process.

19. Applications of the Doppler Effect: 1.Bats navigate by emitting high frequency sound waves (ultrasonic) and then detecting the reflected waves… An example: Imagine the bat and the moth flying towards each other. The moth will “receive” a frequency that is ______than the bat’s emitted frequency. When the sound reflects off the moth, the moth now acts as a “new source” and the bat is the receiver  a 2 nd doppler shift!! The frequency of this “new source” for the 2 nd doppler shift will be the frequency received or heard by the moth from the 1 st doppler shift. higher

20. The frequency received by the bat will be even ________ than the frequency the moth “heard.” The bat’s brain then “calculates” the speed and direction of the moth’s motion from the difference in the emitted and received frequencies… lunch! An interesting bat fact: The bat “hears” best at 83,000Hz, so it actually adjusts the frequency of the waves it sends out so that the doppler-shifted waves it receives back are at 83,000Hz. It’s CRAZY! higher

21. 2. Dolphins hunt underwater by emitting ultrasonic sounds and detecting the reflections. 3. RADAR- RAdio Detecting And Ranging All waves (not just sound) can be doppler shifted. A police radar gun bounces a high frequency radio wave off of a moving car. The system then calculates the speed of the car by comparing the frequency of the emitted “radar” waves with the frequency of the reflected waves. … just like the bat, there are ___ doppler shifts. 2

23. What happens when the velocity of the “source” = the velocity of sound (at the “sound barrier” )? Look at the last picture… All the sound waves line up at the right edge. ____________ interference, then, produces one massive sound wave. Since sound waves are just pressure waves in the air, this causes a tremendous stress on the object as it breaks through the “sound barrier.” Animation: At the sound barrier V=V sound Constructive

24. So, what if the source is moving faster than the speed of the waves themselves, which are moving at the speed of sound? A __________________ occurs!! Animation: Sonic Boom

25. So what is the famous “sonic boom”? Does it only happen as the sound barrier is crossed? ____! What happens after a plane has passed the sound barrier and is now moving faster than v sound ? To visualize it, think about a boat in the water. If the boat travels faster than the water waves, it continually produces a “_____” behind the boat in a __-shape. If you were swimming in the water and the boat went by you, you’d “bob” up and down as the “wake” passed by. NO wake V

26. This is just like a sonic boom…Instead of overlapping circles producing a “v-shaped bow wave”, overlapping ________ produced by an airplane flying faster than the speed of sound, will produce a “_____-shaped shock wave”. The airplane continually carries this wave of intense pressure behind it, and thus continually produces what is known as a sonic boom. When the cone reaches you, you hear the loud “boom,” and then it passes by and reaches your neighbor, and then they hear a loud “boom”… The object itself does NOT even have to make a sound to produce the pressure build-up and the “boom”! The waves all overlap on the outer edge to form a cone shape. Mach cone spheres cone

27. Mach # The mach # is the multiple of the speed of sound For example, if a supersonic aircraft is flying at “Mach 2”, it is traveling at ________ = _____m/s) As the mach number increases (faster moving spacecraft) the angle of the cone ___________ (in other words, the “V” becomes more _______) Examples: Supersonic aircraft, thunder, and the tip of a a whip… 340 x 2680 decreases narrow

28. The figure at left is a photograph of a bullet traveling at Mach 2.45. The mach cone is quite noticeable. A supersonic aircraft actually always produces two sonic booms, one from the aircraft's nose and the other from its tail, but you typically only hear 2 from the space shuttle, since it is so large.

29. We have already discovered some of the properties of oscillations in our slinky lab. Nearly all objects, when hit or struck or plucked or strummed or somehow disturbed, will vibrate. Oscillations are really just a vibrations or repetitive variations. How do we create these oscillations? By applying a small force at regular intervals. (Example: Mass on a Spring) Oscillations (Simple Harmonic Motion)

30. Natural Frequency When objects vibrate they tend to vibrate at a particular frequency or a set of frequencies. The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object. If the amplitude of the vibrations are large enough and if natural frequency is within the human frequency range, then the vibrating object will produce sound waves humans can hear.

31. All objects have a natural frequency or set of frequencies at which they vibrate or oscillate. For example, A pendulum (or a swing) will swing back and forth at a natural frequency that depends only on its _______. length The shorter the stick, the ______ the natural frequency (same as buildings … the taller the building, the ______ the natural frequency… the period, T, is about 10 seconds for tall skyscrapers!) higher lower

32. Resonance So, in summary, when a system is “driven” at its natural frequency (forces applied in rhythm with the natural frequency), the oscillations get bigger. THIS is termed ______________. Without resonance we wouldn't have radio, television, music, or swings on playgrounds, not to mention cool gismos like Tesla coils resonance

33. It is possible for an object to have more than one natural (or resonant) frequency. Usually the natural frequency is the ___ harmonic (fundamental frequency), but other harmonics can be produced as well… Examples: 1. Buildings in the wind (or because of an earthquake) can vibrate at more than 1 natural frequency. Higher harmonics are possible…. Fundamental Frequency Higher Harmonic The top of the building is free to move in the wind. The simplest thing the building can do is sway back and forth. The bottom of the building is fixed to the ground and cannot move. It is therefore a vibrational node. nodes 1st

34. In the Mexico City earthquake of 1985, according to the USGS, “a large percentage of the buildings which were damaged in Mexico City were between 8 and 18 stories high.” WHY? The frequency of the earthquake wave must have been close to one of the ___________________ of the buildings, producing __________. In the USGS’s own words, this “indicates possible resonance effects with dominant two-second period horizontal ground accelerations which were recorded in the area.” natural frequencies resonance

35. 2. The Tacoma Narrows Bridge (nicknamed “Galloping Girtie”) collapsed in 1940… Wind caused the bridge to begin vibrating at one of its natural frequencies …a torsional wave developed …. amplitude increased…. and the bridge eventually tore itself apart….. Resonance in action!! Video…