Q: Monochromatic light falls on two narrow slits that are 0.05 mm apart. On a screen 4.00 m away, the first order fringe (bright spot) is 6.00 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 mm apart. On a screen 4.00 m away, the first order fringe (bright spot) is 6.00 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 nm falls on two narrow slits that are 0.04 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 nm?

Accepted Answer

$$175\ 	ext{nm}$$

Question 4

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 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

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

Accepted Answer

$$0.2\ 	ext{m}$$

Question 7

A standing sound wave is shown in a 30 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 m/s. If you run toward your friend at 10 m/s while they play an open pipe with a wavelength of 0.3 m, what frequency will you hear?

Accepted Answer

$$2944\ 	ext{Hz}$$

Question 9

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

Accepted Answer

$$343\ 	ext{m}$$

Question 10

A monoatomic ideal gas consisting of $$n$$ moles undergoes a 3-step engine cycle. The first step from A to B is isobaric from $$(P_1$, V_1$) to$$ $$(P_1$, 2V_1). $$The second step from B to C is isovolumetric from $$(P_1$, 2V_1) to$$ $$(P_2$, 2V_1)$$ where $$P_2$$ \u003c $$P_1. $$The third step from C back to A is adiabatic compression. What is the ratio $$\frac{P_2$}{P_1$}$$?

Accepted Answer

$$0.63$$

Question 11

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

Accepted Answer

Step A to B (isobaric expansion)

Question 12

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

Accepted Answer

$$0.37$$

Question 13

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

Accepted Answer

$$nR \ln 2$$

Question 14

A thin film of oil ($$n=1.50) on $$water ($$n=1.33) is $$illuminated with light of wavelength 600 nm. What is the minimum thickness for destructive interference?

Accepted Answer

$$200\ 	ext{nm}$$

Question 15

A string is fixed at both ends and vibrates in its second harmonic. If the string is 1.2 m long and the speed of waves on the string is 60 m/s, what is the frequency?

Accepted Answer

$$50\ 	ext{Hz}$$

Question 16

A sound wave in air has an intensity of $$1 	imes 10$$^{-6}$$\ 	ext{W/m}^2. $$What is the sound level in decibels?

Accepted Answer

$$60\ 	ext{dB}$$

Question 17

A gas undergoes an isothermal expansion from $$V_1 to$$ $$2V_1 at $$temperature $$T. $$What is the work done by the gas?

Accepted Answer

$$nRT \ln 2$$

Question 18

A refrigerator removes 500 J of heat from its interior and expels 700 J to the surroundings. What is its coefficient of performance (COP)?

Accepted Answer

$$1.4$$

PHY222 Midterm #2 Study Guide: Waves, Sound, and Thermodynamics

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