Waves transfer energy form one place to another.

Sound Waves carry energy along, not air.

Beat the drum and send energy but not necessarily air molecules from transmitter to receiver. The actual air from the drum arrives much later than the sound.

Sound speed depends upon the medium. With an explosion, you feel the vibrations through the ground before you hear the blast. The speed of sound in the ground is faster than in air, ergo you feel those vibrations with your entire body.

Waves: A very important relationship for sound and music:

Waves has several fundamental properties, meaning "things that all (types of) waves do...." Some of these are:

• transfer energy
• obey Huygens's principle
• reflect
• refract
• interfere (superimpose)
• diffract
• add to create beats
• exhibit the 'Doppler effect
• add to create other waveshapes (Fourier)

Huygen's principle...each point on a wavefront acts as a source of circular (spherical) waves."

In terms of straightforward propagation of circular or plane waves, one can imagine each point on the wave as a source of circular waves, propagate froward and draw a line tangent to each front to get the propagating wavefront.

Wave Reflections on string:

Demos in class included wave reflections on a long spring, a torsion wave apparatus, and a rubber rope. Thi is a simulation you can play with. Note that fixed end reflections are inverted and open end reflections are not.

Wave Pulse Reflections.: To see rflected waves, lower the damping setting. SCompare reflected waves fgorfixed and open ends. Play around and have fun!

Woks well shopwing waves reflected on a string.

BOOK ERROR: PAGE 44 Top paragraph describing sound waves in a tube. The logic is backwards. An open ended tube is like a fixed string end and a closed end tube acts like an open ended string. Think of the open ended tube as an end FIXED AT ATMOSPHERIC PRESSURE. So the reflected wave inverts at an open ended tube, like the string wave inverts at a a fixed ended string.

refract

Refraction is a fancy word for bending of waves. All waves refract when the pass from one medium to another.... as long as their wave speed changes between media.

Eyeglasses are designed to exploit this phenomenon for light waves. The light waves effectively travel at slower speeds through the glass or plastic in the eyeglass lenses. This causes them to bend and pre-focus light before it passes into weak eyes.

You may have experienced hearing sounds from far away-- across a lake for example-- because the sound waves bent (refracted) in passing over cool air above the lake.

What is the assumption about how sound wave speed changes with temperature that is implicit in this image? Does this make sense?

Why is the speed of sound faster in warmer air? (hint: think about the characteristics of oscillators that we wrote on the board on Tuesday)

One way to conceptualize how waves bend in passing between different media is to think of a row of marching band members passing from a dry zone into mud on a football field:

The top image shows the direction of a sound wave comfing from the upper left, and passing into a material where it slows down. The result is a reflected wave (lower left) and a refracted wave (right-hand side), which is bent towards the perpendicular to the interface.

As the left-hand members of the marching band (upper "x's") encounter the muddy zone, they slow down. Other members of the line of band members (lower "x's") encounter the zone later and slow down then. The result is a bending of the direction of the band member "wave."

interfere (superpose)

Time to pull out the fabulous waveinterference applet again. We can set up two sources of our water, sound and light waves and "see" how they interfere.

http://phet.colorado.edu/en/simulation/wave-interference

Let's explore this simulation using a detector. Here are some questions we can try to answer:

What is the wavelength of wave from a single source? (we can pause the simulation and use the measuring tape to measure peak-to-peak) {how does it vary with frequency (note: can you Add detector and measure frequency from the detector graph?)?}

Now let's look at 2 sources.

Does the wavelength of the waves change when adding a second source?

What are our assumptions about the sources?

Using sound wave sources and the detector, explore the sonic field around the speakers. Are there dead spots and live spots? Is the sound wavelength the same everywhere? {one can also use the fabulous PhET sound applet to 'listen' to the sonic field.

What does separating the source speakers do to the sonic field? Imagine yourself sitting at the right-hand side of the (shown) field listening to your stereo. For a given frequency of tone, how does changing the speaker separation affect what you hear?

What does changing the frequency do to the sonic field? For a given speaker separation, how does changing the frequency affect what you hear?

Let's do this with real speakers and hear what two-speaker interference sounds like.

 

 

Addition of Waves

One of the most important properties of waves is that they add (superpose" or in) when occupying the same space. The following link (courtesy of University of Liverpool) shows how two equal-amplitude, equal-frequency waves interfere constructively or destructively when occupying the same space. (This was clearly important when we considered wave interference above.)

Let's consider how this works at the blackboard, then move on to an im-puls-ive demo.

The observation that (equal-wavelength) waves add when they are in phase (constructive interference) and subtract when they are (180 degrees or "pi radians") out of phase (destructive interference) is crucial to understanding many concepts in sound and music. It is also necessary to realize that pulses can both travel along media (ropes, strings, torsion apparatus) and reflect off of boundaries.

Beyond the stereo interference examples, above, this concept of wave addition is important in understanding standing waves and things like organ pipe resonance which we will examine in the next chapter. It is also useful in explaining beats.

Beats

Once we have established that two equal-wavelength waves passing a point will add (or subtract/destructively interfere), we can move on to asking a few more questions:

Phase of the two wavelets is important. How does this relate to timing of the initiation of the two waves

How does the amplitude of the two waves affect this process

What happens to the motion point in the media (string, rope, air pressure at a point) when the waves aren't the same frequency? What do you think will happen under these circumstances

Let's consider how this works by first examining a groovy applet, then move on to a demonstration of beats.

This helps us answer our question about the sound quality of Balinese Gamelan orchestras.

It is also useful for musicians. We use our ability to hear beats between our instruments and a "reference tone" to help us tune up!

 

Doppler effect

Have you ever waited for a train to cross and notice how the sound of its "whistle" changes as it approaches and then recedes from you?

 

This is called the doppler effect. It is caused because the sound source, the train in this case, is first moving towards you and then away from you.

Any wave phenomenon can exhibit the doppler effect, as long as the source is moving towards or away from the observer. Light from distant stars is doppler-shifted (generally towards lower frequencies {red-shifted}. This is one way astrophysicists can tell that the universe is expanding.

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