Q: Monochromatic light falls on two narrow slits that are $$0.05\ \text{mm}$$ apart. On a screen $$4.00\ \text{m}$$ away, the first order fringe (bright spot) is $$6.00\ \text{cm}$$ from the middle of the interference pattern. What is the wavelength of the light?

$$5.0 \times 10$$^{-7}$$\ \text{m}$$

Question 1

Monochromatic light falls on two narrow slits that are $$0.05\ 	ext{mm}$$ apart. On a screen $$4.00\ 	ext{m}$$ away, the first order fringe (bright spot) is $$6.00\ 	ext{cm}$$ from the middle of the interference pattern. What is the wavelength of the light?

Accepted Answer

$$5.0 	imes 10$$^{-7}$$\ 	ext{m}$$

Question 2

Monochromatic light of wavelength $$500\ 	ext{nm}$$ falls on two narrow slits that are $$0.04\ 	ext{mm}$$ apart and this generates 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 3

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 $$700\ 	ext{nm}$$?

Accepted Answer

$$175\ 	ext{nm}$$

Question 4

A soap film ($$n=1.35) of $$thickness $$150\ 	ext{nm} is $$surrounded by air ($$n=1.00) on $$both sides. If light of a certain wavelength is beamed at the soap film such that it hits the 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 5

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

$$1.2\ 	ext{m/s}$$

Question 6

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

Accepted Answer

$$0.33\ 	ext{s}$$

Question 7

A standing sound wave is shown in a $$30\ 	ext{cm}$$ long open tube. What is the wavelength of the standing wave?

Accepted Answer

$$30\ 	ext{cm}$$

Question 8

Assume the speed of sound in air is $$343\ 	ext{m/s}. If $$you run toward a stationary friend playing an open pipe with a wavelength of $$0.30\ 	ext{m} at$$ $$10\ 	ext{m/s}$$, what frequency will you hear?

Accepted Answer

$$2944\ 	ext{Hz}$$

Question 9

Two wind pipes are played together, one at $$1143\ 	ext{Hz}$$ and the other at $$1146\ 	ext{Hz}. $$What is the wavelength that corresponds to the beat frequency generated by these two instruments? (Speed of sound is $$343\ 	ext{m/s}.)$$

Accepted Answer

$$114\ 	ext{m}$$

Question 10

A monoatomic ideal gas undergoes a three-step engine cycle. The first step is isobaric expansion from $$(P_1$, V_1$) to$$ $$(P_1$, 2V_1). $$The second step is isochoric cooling from $$(P_1$, 2V_1) to$$ $$(P_2$, 2V_1). $$The third step is adiabatic compression back to $$(P_1$, V_1$). $$What is the ratio $$P_2$$/$$P_1$$ after the adiabatic compression?

Accepted Answer

$$0.63$$

Question 11

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

Accepted Answer

The isobaric expansion from $$A to$$ $$B$$

Question 12

For the same engine cycle, what is the efficiency of the engine? (Give your answer to two significant digits.)

Accepted Answer

$$0.37$$

Question 13

A soap film (n=1.33) is illuminated with white light at normal incidence. Which wavelength in the visible spectrum will be most strongly reflected if the film thickness is $$200\ 	ext{nm}$$?

Accepted Answer

$$532\ 	ext{nm}$$

Question 14

A string is fixed at both ends and vibrates in its third harmonic. If the length of the string is $$1.2\ 	ext{m}$$ and the wave speed is $$60\ 	ext{m/s}$$, what is the frequency of the third harmonic?

Accepted Answer

$$75\ 	ext{Hz}$$

Question 15

A sound wave in air has an intensity of $$1.0 	imes 10$$^{-6}$$\ 	ext{W/m}^2. $$What is the corresponding sound level in decibels (dB)?

Accepted Answer

$$60\ 	ext{dB}$$

Question 16

A gas undergoes an isothermal expansion at temperature $$T. $$What is the change in internal energy of the gas during this process?

Accepted Answer

$$0$$

Question 17

A refrigerator removes $$500\ 	ext{J} of $$heat from its interior and expels $$600\ 	ext{J} to $$the room. What is its coefficient of performance (COP)?

Accepted Answer

$$0.83$$

Question 18

A transverse wave on a string is described by $$D(x,t) = 0.02\sin(4\pi x - 100\pi t)$$, where $$x$$ and $$t$$ are in SI units. What is the maximum transverse velocity of the string?

Accepted Answer

$$2\ 	ext{m/s}$$

PHY222 Midterm #2 Study Guidance: Waves, Interference, and Thermodynamics

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