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4D: How Light and Sound Interact With Matter

Waves bending, cancelling, echoing and being absorbed: sound and ultrasound, optics and the eye, and the spectroscopy that reads molecules.

17 topics · 74 questions

Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.

4D. Production of Sound, Its Speed in Media, and Pitch

  1. How it worksHow does a vibrating surface squeeze and stretch the air into travelling bands of pressure?
  2. How it worksHow does sound sprint through steel, slow down in water and crawl slowest of all through air?
  3. Worked exampleFind how long thunder takes to arrive from a strike 1.5 km away when sound travels at 343 m/s.
  4. Common mistakeWhy isn't sound faster in air than in water given how much thinner air is?
  5. Going furtherWhat happens to a string's pitch when you tighten it, shorten it, or swap it for a thicker one?
Your turneasy1 of 3
You see a lightning flash and hear the thunder 9 seconds later. Sound travels at 340 m/s in the air that day. Find the distance to the strike, in meters.

4D. Sound Intensity, Decibels, and Attenuation

  1. How it worksHow does the decibel scale squeeze a trillionfold range of intensity onto a ruler from 0 to 120?
  2. Worked exampleFind the decibel level of a sound 1000 times more intense than the threshold of hearing.
  3. How it worksHow does intensity fall off with the square of distance as a wave spreads over a growing sphere?
  4. Worked exampleFind how many decibels the reading drops when a source moves from 2 m away to 20 m away.
  5. Common mistakeWhy isn't a jump from 40 to 80 decibels a doubling of the sound?
Your turneasy1 of 3
A sound carries an intensity 108 times the threshold of hearing. Find its sound level, in decibels.

4D. The Doppler Effect

  1. How it worksHow does a moving source bunch its wavefronts up in front and stretch them out behind?
  2. How it worksHow does a listener running into the waves sweep through more crests per second and hear it higher?
  3. Worked exampleFind the pitch heard from a 500 Hz siren closing at 30 m/s when sound travels at 340 m/s.
  4. Worked exampleFind the frequency shift a Doppler probe reads from red cells moving at 0.50 m/s toward it.
  5. Common mistakeWhy isn't the pitch of an approaching ambulance climbing higher and higher as it nears?
Your turnmedium1 of 3
An ambulance siren sounding a steady 618 Hz drives straight toward a stationary listener at a speed equal to 1/7 of the speed of sound in air. Find the frequency the listener hears, in Hz.

4D. Resonance and Standing Waves in Pipes and Strings

  1. How it worksHow do a wave and its own reflection lock into a standing pattern whose nodes never budge?
  2. How it worksHow does closing one end of a pipe drop its lowest note an octave and erase the even harmonics?
  3. Worked exampleFind the three lowest resonant frequencies of a 0.68 m pipe closed at one end in 340 m/s air.
  4. Going furtherWhat happens to a wine glass when a sustained tone lands exactly on its natural frequency?
Your turneasy1 of 3
An organ pipe 65 cm long is closed at one end. Sound travels at 340 m/s in the air inside it. Find its fundamental frequency, in Hz.

4D. Ultrasound and Shock Waves

  1. How it worksHow does the round-trip time of an echo convert into the depth of whatever bounced it back?
  2. How it worksHow does a source outrunning its own sound stack the wavefronts into a cone-shaped shock?
  3. Worked exampleFind the tissue depth that sends back an echo after 40 microseconds at 1540 m/s.
  4. Common mistakeWhy isn't an ultrasound scan simply an X-ray taken with sound instead of radiation?
  5. Ties togetherHow do echo delay and Doppler shift combine to map blood speed inside a beating heart?
Your turneasy1 of 3
An ultrasound pulse returns from a tissue boundary 90 microseconds after it is sent. Sound travels at 1500 m/s in that tissue. Find the depth of the boundary, in centimeters.

4D. Properties of Electromagnetic Radiation and the Spectrum

  1. How it worksHow do an electric field and a magnetic field take turns regenerating each other as light moves?
  2. Worked exampleFind the energy carried by one photon of green light at a wavelength of 500 nanometers.
  3. How it worksHow does the spectrum line itself up by frequency from radio through visible on up to gamma?
  4. Common mistakeWhy isn't a brighter beam of red light made of higher-energy photons?
  5. Going furtherWhat happens to light's wavelength and speed on entering glass while its frequency refuses to change?
Your turneasy1 of 3
Find the energy, in electron volts, of a photon of wavelength 687 nm. Use hc = 1240 eV nm.

4D. Interference and Young's Double-Slit Experiment

  1. How it worksHow does a path difference of half a wavelength turn two crests into perfect cancellation?
  2. Worked exampleFind the bright-fringe spacing for 600 nm light through slits 0.10 mm apart on a screen 2.0 m away.
  3. Common mistakeWhy isn't the central bright band of a double-slit pattern produced by one slit overpowering the other?
  4. Going furtherWhat happens to the spacing of the fringes when the two slits are pushed farther apart?
Your turnmedium1 of 3
Light of wavelength 609 nm falls on a pair of slits separated by 4 times 0.10 mm, and the fringes appear on a screen 4 m away. Find the spacing between adjacent bright fringes, in millimeters.

4D. Diffraction, Thin Films, and Gratings

  1. How it worksHow does a wave bend around a sharp edge and spill into the shadow it should never reach?
  2. How it worksHow does light reflecting off the back of a thin film come back out of step and erase one color?
  3. Worked exampleFind the angle of the first-order maximum for 500 nm light on a grating ruled 5000 lines per cm.
  4. Going furtherWhat happens when an X-ray beam meets a crystal whose atomic spacing matches its wavelength?
Your turnmedium1 of 3
A diffraction grating ruled with 6 thousand lines per centimeter is lit by 595 nm light. Find the sine of the angle at which the first-order maximum appears.

4D. Polarization of Light

  1. How it worksHow does a polarizing filter pass only the slice of the electric field lined up with its axis?
  2. Worked exampleFind the fraction of an unpolarized beam that survives two filters set 60 degrees apart.
  3. Common mistakeWhy isn't unpolarized light just light whose electric field points nowhere in particular?
  4. Going furtherWhat happens to the beam when a second polarizer is rotated 90 degrees against the first?
Your turnmedium1 of 3
Unpolarized light of intensity 303 W/m2 strikes an ideal polarizer, and a second ideal polarizer stands with its axis 60 degrees from the first. Find the intensity leaving the second polarizer, in W/m2.

4D. Infrared Spectra and Characteristic Group Absorptions

  1. How it worksHow does a bond act like two masses on a spring whose stiffness fixes the absorption frequency?
  2. Worked exampleFind which functional groups are present from a broad 3300 band plus a sharp 1710 peak.
  3. Common mistakeWhy isn't every bond in a molecule capable of absorbing infrared light?
  4. Going furtherWhat happens to a carbonyl stretch when the carbonyl is pulled into a conjugated system?
Your turnhard1 of 3
An IR spectrum shows a very broad band centered near 3209 cm−1 together with a strong sharp peak at 1719 cm−1. Which compound best fits it?

4D. UV-Visible Absorption, Conjugation, and Color

  1. How it worksHow does a π electron leaping to an antibonding orbital soak up one precise wavelength?
  2. How it worksHow does stacking more conjugated double bonds drag absorption toward longer wavelengths?
  3. Common mistakeWhy isn't a compound's color the same as the color of the light it absorbs?
  4. Worked exampleFind the apparent color of a solution whose absorption peak sits at 450 nanometers.
Your turneasy1 of 3
A dye solution shows a single strong absorption peak at 458 nm and is otherwise transparent across the visible range. What color does the solution appear?

4D. NMR: Equivalent Protons and Spin-Spin Splitting

  1. How it worksHow does the electron cloud around a proton shield it and slide its peak upfield?
  2. Worked exampleFind the number of signals and the splitting pattern expected in the NMR of ethyl acetate.
  3. How it worksHow does the n plus 1 rule turn neighboring protons into a doublet, a triplet or a quartet?
  4. Common mistakeWhy isn't the area under an NMR peak telling you how many neighbors a proton has?
Your turneasy1 of 3
A proton in a molecule has 4 equivalent protons on the neighboring carbon and none anywhere else nearby. Find the number of lines its NMR signal is split into.

4D. Reflection and Spherical Mirrors

  1. How it worksHow does the law of reflection send every incoming ray back out at the angle it arrived?
  2. How it worksHow do parallel rays striking a concave mirror all funnel through one focal point?
  3. Common mistakeWhy isn't a virtual image something you could catch on a sheet of paper?
  4. Worked exampleFind the image distance and magnification for an object 30 cm from a concave mirror of focal length 10 cm.
Your turnmedium1 of 3
An object is placed 5 focal lengths in front of a concave mirror whose focal length is 18 cm. Find the image distance, in cm, taking a real image in front of the mirror as positive.

4D. Refraction, Snell's Law, and Dispersion

  1. How it worksHow does one edge of a wavefront slowing down first swing the whole wave onto a new heading?
  2. How it worksHow does each color bending by a slightly different amount fan white light out into a rainbow?
  3. Worked exampleFind the angle inside the water when light strikes the surface at 30 degrees from air, with n of 1.33.
  4. Common mistakeWhy isn't light bending at glass because it is hunting for the shortest route through?
Your turneasy1 of 3
Light travels at 3.0 x 108 m/s in vacuum. Find its speed inside a medium of refractive index 2.11, in units of 108 m/s.

4D. Total Internal Reflection

  1. How it worksHow does the refracted ray swing out toward 90 degrees and then vanish altogether as the angle grows?
  2. Worked exampleFind the critical angle for light trying to escape from water of index 1.33 into air.
  3. Common mistakeWhy isn't total internal reflection available to light going from air into glass?
  4. Going furtherWhat happens inside a fiber optic strand that keeps light trapped around every bend?
Your turnmedium1 of 3
Light inside a material of refractive index 2.1 reaches a boundary with a medium of refractive index 1.227. Find the sine of the critical angle.

4D. Thin Lenses, the Lens Equation, and Magnification

  1. How it worksHow do the three principal rays leaving one point all reconvene at a single image point?
  2. How it worksHow do the sign conventions in one over p plus one over q equals one over f label an image real or virtual?
  3. Worked exampleFind the image distance and magnification for an object 15 cm from a converging lens of focal length 10 cm.
  4. Worked exampleFind the power in diopters of a lens whose focal length is 25 centimeters.
  5. Common mistakeWhy isn't covering half of a lens enough to wipe out half of the image?
Your turnhard1 of 3
An object stands 20.5 cm from a thin converging lens of focal length 16 cm. Find the image distance, in cm, counting a real image on the far side of the lens as positive and a virtual image on the near side as negative.

4D. Lens Combinations, Aberration, and the Human Eye

  1. How it worksHow does the first lens in a row hand its image to the second lens as a brand new object?
  2. How it worksHow does the ciliary muscle reshape the lens to drag a near object into focus on the retina?
  3. Worked exampleFind the corrective lens power a nearsighted eye needs when its far point is 50 centimeters.
  4. Ties togetherHow does the same bending that snaps a straw at a water surface set the cornea's focusing power?
Your turnmedium1 of 3
A nearsighted eye can focus clearly on nothing farther away than 62 cm. Find the power, in diopters, of the corrective lens it needs.

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