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Teachers & SchoolsStudy Guide

1. What is the difference between a traveling wave and a standing wave?

*Answer*: Traveling waves are a periodic disturbance that moves through some medium—air, space, vacuum—transferring energy from one point to another. Light, sound, and ocean waves are all examples. Standing waves are a pattern of motion that oscillates in place, without transferring energy from one point to another. The moving patterns in vibrating guitar strings are an example.

2. What is the difference between a transverse and a longitudinal wave?

*Answer*: Both are traveling waves, but oscillate in different directions as they move. A transverse wave oscillates orthogonally to its direction of movement—for example, as ripples spread laterally across a pond, the water moves up and down. A longitudinal wave oscillates in the same direction as it moves—sound waves that emanate from a speaker push air back and forth in the same direction as the speaker's cone movement.

3. What are the characteristics of simple harmonic motion?

*Answer*: Simple harmonic motion is a specific form of periodic, repeated motion that has a constant frequency, a constant amplitude, and can be described easily by a sine or cosine function.

4. What is the difference between frequency and angular frequency?

*Answer*: Frequency describes how many times per second a motion happens—a tuning fork that vibrate 440 times in one second has a frequency of 440 Hz. Angular frequency describes the same thing, but in different units. It translates a full cycle of motion into 360º (or, more commonly, 2π rad) and tracks cycles per second by measuring how many "radians" of movement occur per second. Using ω instead of *f* greatly simplifies any wave equation by removing factors of 2π needed to make the trig functions work out correctly.

5. Is it correct to measure wavelength from the zero point of one waveform to the next zero point? From crest to crest? Trough to trough?

*Answer*: All of these are viable and, if done correctly, will yield the same (correct!) wavelength value. The important thing to remember is to measure from one point of a cycle to *the same exact point* on the next cycle of the wave, whatever that first point may be. Remeber these points need to be multiples of 2π from one another.

6. What happens when a noisy object moves faster than the speed of sound?

*Answer*: When an object—like, say, a jet—moves faster than the speed of sound in air (about 340 m/s, or 760 mph), it literally outruns the sound waves it creates. This is beyond a normal Doppler shifting of frequency: the jet will pass you before you hear it coming, meaning it's gone *supersonic*. As the sound waves try to catch up, they end up all overlapping, creating a high pressure shockwave that is much louder than any of the sound waves individually. After the jet passes, you hear this shockwave—loudly—as a *sonic boom*.

7. Why does the Doppler Effect make an approaching noise sound higher? Or make a receding noise sound lower?

*Answer*: As the noise moves towards you, the wavefronts of the sound wave appear closer together, since each successive wavefront is emitted closer and closer to you. If the wavefronts are closer together, the frequency appears to increase, making the sound higher in pitch. As a noise moves away from you, the opposite happens: the wavefronts appear further apart, since each successive wavefront is emitted further and further away from you. Further apart wavefronts makes the frequency appear to decrease, leading to a sound that is lower in pitch.

8. What are the necessary conditions for two interfering traveling waves to combine to make a standing wave?

*Answer*: The waves must be traveling in opposite directions and have equal amplitudes and frequencies in order to produce a standing wave pattern.

9. Does higher frequency light have a longer or shorter wavelength than lower frequency light?

*Answer*: All light travels at the same speed *c*, where, according to our formula for wave velocity, *c* = *f*λ. This means *f* and λ are inversely proportional, so higher frequency light (like blue light) has a shorter wavelength than lower frequency light (like red light).

10. What does it mean for waves to be "in phase" with one another?

*Answer*: For waves to be in phase, they either must have the same phase value (φ), or values of φ that are multiples of each other, allowing the wave's cycles to overlap perfectly.