What kind of disturbance is produced when we drop a pebble in a pond? Ripples move outward in a _______. How do sound waves travel? They move outward in _________. A 2-D representation of a stationary fire truck sounding its sirens….. Animation: circle spheres

What happens if the source of the sound is moving (say if the fire truck is moving to the right?) 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 the moving truck) would hear sound waves that have a ________ wavelength, and, thus, a ______ frequency. Animation: shorter higher longerlower

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

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

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)

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

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

An Example: Mr. Restad is late for work, so he’s driving 44m/s (100mph!!) down the interstate. He passes Joe Policeman who is driving towards Mr. Restad at a poky 30m/s (65 mph) If the actual frequency of the police siren is a high “C” of 512 Hz, what frequency does Reid hear as he is driving towards the police car? Should the frequency be higher or lower as a result of Restad’s (the receiver) motion towards the siren? _________, so the sign in the numerator is ____. Should the frequency be higher or lower as a result of the source (siren) moving toward Mr. Restad? _________, so the sign in the denominator is ____. 44 m/s30 m/s higher + -

The answer… What frequency would Mr. Restad hear after he passes the police car? Try this one yourself…. 44 m/s 30 m/s

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

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

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

RED shift Blue shift

Light experiences the Doppler effect too! Objects that are moving quickly away from us have their wavelength shifted toward the RED end of the spectrum Objects that are movingquickly toward us have their wavelength shifted toward the BLUE end of the spectrum

4. National Weather Service uses “Doppler Radar” to detect severe storms. Radar pulses sent out reflect off water droplets and return, where the received frequency is measured and compared to the emitted frequecy. Using Doppler shift equations, the ______ and _________ of the air masses can be determined, as well as the amount of precipitation. NEXRAD = NEXt Generation Weather RADar Doppler Radar for Hurricane Katrina speeddirection higher lower

Most weather radars, including NEXRAD, transmit and receive radio waves with a single, horizontal polarization. That is, the direction of the electric field wave crest is aligned along the horizontal axis. Polarimetric radars transmit and receive both horizontal and vertical polarization radio wave pulses. Therefore, they measure both the horizontal and vertical dimensions of cloud and precipitation particles. This additional information leads to improved radar estimation of precipitation type and rate.horizontalvertical

A little Riddle… On October 14, 1947, a man broke something in California that could NOT be repaired. He continued to break the thing on a regular basis, as did others. What did the man break, AND what was his name? Many before and even after him died trying. Why? What happens when an aircraft flies at the speed of sound? Chuck Yeager became the first human to break the sound barrier… in a rocket- powered aircraft.

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

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

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

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

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

The figure at left is a photograph of a bullet traveling at Mach 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.