Question 1

Monochromatic light of wavelength 500 nm falls on two narrow slits that are 0.04 mm apart, generating an interference pattern on a distant screen. At what angle (in degrees) does the first minima occur in the interference pattern?

Accepted Answer

$$1.07^{\circ}$$

Question 2

A light beam traveling through air ($$n=1.00) $$reflects perpendicularly off the top and bottom surfaces of a thin layer of oil ($$n=1.50) $$floating on water ($$n=1.33). $$What is the thinnest layer of oil that will give rise to constructive interference at a wavelength of 700 nm?

Accepted Answer

$$175\ 	ext{nm}$$

Question 3

A soap film ($$n=1.35) of $$thickness 150 nm is surrounded by air ($$n=1.00) on $$both sides. If light of a certain wavelength is beamed at the soap film perpendicular to its surface, what is the longest wavelength of light for which you’ll see no reflection?

Accepted Answer

$$600\ 	ext{nm}$$

Question 4

The displacement of a transverse wave on a string is given by $$D(x,t)=4\sin(5\pi x-6\pi t). $$What is the speed of the traveling wave?

Accepted Answer

$$0.83\ 	ext{m/s}$$

Question 5

For the wave $$D(x,t)=4\sin(5\pi x-6\pi t)$$, what is the wavelength?

Accepted Answer

$$0.4\ 	ext{m}$$

Question 6

A standing sound wave is shown in a 30 cm long open tube. What is the wavelength of the standing wave?

Accepted Answer

$$15\ 	ext{cm}$$

Question 7

Assume the speed of sound in air is $$343\ 	ext{m/s}. If $$you run toward your friend at $$10\ 	ext{m/s}$$ while they play an open pipe with a wavelength of $$15\ 	ext{cm}$$, what frequency will you hear?

Accepted Answer

$$2944\ 	ext{Hz}$$

Question 8

Two wind pipes generate frequencies that differ by $$3\ 	ext{Hz}. $$What is the wavelength that corresponds to the beat frequency generated by these two instruments?

Accepted Answer

$$343\ 	ext{m}$$

Question 9

A monoatomic ideal gas consisting of $$n$$ moles undergoes a 3-step engine cycle. The first step from A to B is a constant pressure process from $$(P_1$, V_1$) to$$ $$(P_1$, 2V_1). $$The second step from B to C is a constant volume process from $$(P_1$, 2V_1) to$$ $$(P_2$, 2V_1)$$ where $$P_2$$\u003cP_1$$. The third step from C back to A is an adiabatic compression. What is the ratio $$\frac{$$P_2$$}{$$P_1$$}$$ for the adiabatic process?

Accepted Answer

$$0.37$$

Question 10

For the engine cycle described above, which step corresponds to the heat absorbed from the high temperature reservoir ($$Q_H$$)?

Accepted Answer

Step A to B (isobaric expansion)

Question 11

For the engine cycle described above, what is the efficiency of the cycle (to two significant digits)?

Accepted Answer

$$0.37$$

Question 12

For the engine cycle described above, what is the change in entropy for the isobaric process from A to B?

Accepted Answer

$$nR\ln(2)$$

Question 13

A transverse wave on a string is described by $$D(x,t)=A\sin(kx-\omega t). $$What is the direction of propagation of the wave?

Accepted Answer

Positive x-direction

Question 14

Which of the following wave functions best describes the displacement for a standing wave in an open tube?

Accepted Answer

$$A\sin(kx)\cos(\omega t)$$

Question 15

A thin film of oil ($$n=1.50) on $$water ($$n=1.33) is $$illuminated with light of wavelength $$700\ 	ext{nm}. $$For constructive interference, what is the minimum thickness of the oil film?

Accepted Answer

$$175\ 	ext{nm}$$

Question 16

A soap film ($$n=1.35) of $$thickness $$150\ 	ext{nm} is $$surrounded by air ($$n=1.00). $$For destructive interference, what is the longest wavelength of light for which you’ll see no reflection?

Accepted Answer

$$600\ 	ext{nm}$$

Question 17

A string is vibrating in its second harmonic. If the length of the string is $$L$$, what is the wavelength of the standing wave?

Accepted Answer

$$L$$

Question 18

A sound wave travels through air at $$343\ 	ext{m/s}. If $$the frequency is $$440\ 	ext{Hz}$$, what is the wavelength?

Accepted Answer

$$0.78\ 	ext{m}$$

PHY222 Midterm Study Guidance: Waves, Interference, Thermodynamics

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