Today 1/24 HW: 1/23 Handout

“Beats and Boundaries” due Wednesday 1/29

Today:Beats 17.4Reflections at Boundaries 27.3

Monday: Thin Film Interference 27.3 Labs start Monday

Next Week’s Lab: Microwaves A wave in the “electric field” Reflection and transmission from and

through wood Reflection from metal (why metal is bad in

your microwave) Polarization (see section 24.6) Interference (Young’s Double Slit)

Beats

Occur when the frequencies of the sources are not the same

Frequencies must be close Locations for constructive interference move

over time Causes sound to get loud and soft fb “beat frequency” depends on source

frequency difference

0.5 s

10 Hz

12 Hz

2 Hz

Sources emitting different frequencies.

Source 1 Source 2

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Source 1 Source 2

Sources emitting different frequencies.

In this case they are alternately in and out of phase as time goes by.

c

Now the locations of constructive (and destructive) interference move in time. A stationary listener hears “Beats.”

Beats

fb = f1 - f2

The beat frequency tells you the difference between the two source frequencies.

You want to know the frequency of a tuning fork. You test it by playing it at the same time as a tuning fork with a known frequency of 342 Hz and you hear beats at a rate of 5 per second. You then play it at the same time as one with a known frequency of 349 Hz and the beats are heard at a rate of 12 per second. What is the frequency of the tuning fork?

a. 347 Hz b. 361 Hz c. 345.5 Hz

d. 337 Hz e. 354 Hz.

Reflections at Boundaries Four situations

Fixed end

Free end

Light to heavy

Heavy to light

Fixed End Reflections

Fixed end

Crest turns into trough

Leading edge is the same

See “Wave Interference” handout for how the string looks during the reflection.

Same velocity, length, and amplitude

Free End Reflections

Free end

Crest stays a crest

Leading edge is the same

See “Wave Interference” handout for how the string looks during the reflection.

Same velocity, length, and amplitude

Light to HeavyBoth transmission and reflection

Boundary feels like a fixed end to the light string

Reflection just like fixed end, inverted

Transmitted wavelength has the same shape except it’s shorter in length because it travels slower than the incoming wave.

Slower, so not as far from boundary

Shorter, “bunched up” Inverted wave

Heavy to LightBoth transmission and reflection

Boundary feels like a free end to the heavy string

Reflection just like free end, not inverted

Faster, farther from boundary

Longer, “spread out” Wave not inverted

Transmitted wavelength has the same shape except it’s longer in length because it travels faster than the incoming wave.

Slower, so not as far from boundary

Shorter, “bunched up” Inverted wave

Faster, farther from boundary

Longer, “spread out” Same as incoming wave

Light: Glass to Air

Light: Air to Glass