Exam 5.3

Microwaves travel with the speed of light, c = 3 × 108 m/s. At a frequency of 10 GHz these waves cause the water molecules in your burrito to vibrate. What is their wavelength?1 GHz = 1 Gigahertz = 109 cycles/sec a) 0.3 mm b) 3 cm c) 30 cm d) 300 m e) 3 km

3 cm

The wave speed goes inversely as the square root of the mass per unit length, which is a measure of the inertia of the rope. So in a thicker (more massive) rope at the same tension, the wave speed will ____.

decrease

`If λ = 1 m, then a shift of 2.5 m corresponds to 2.5λ, which puts the two waves out of phase, leading to ____. The sound intensity will therefore go to zero.

destructive interference

The beat frequency is determined by the ____ and is independent of their actual values.

difference in frequencies

Remember that intensity drops with the _____ , so if intensity drops by a factor of 10, the other person must be √10 farther away, which is about a factor of 3.

inverse square of the distance

A thick string implies a ____ mass per length and a ___ wave speed.

large; small

Two strings are made of the same material and have equal tensions. String 1 is thick; string 2 is thin. Is the speed of waves on string 1 greater than, less than, or equal to the speed of waves on string 2?

less than the speed of waves on string 2

By drinking some of the soda, you have effectively increased the length of the air column in the bottle. A longer pipe means that the standing wave in the bottle would have a longer wavelength. Because the wave speed remains the same, and we know thatv = fλ, then we see that the frequency has to be ____.

lower

The velocity of an oscillating particle is (momentarily) zero at its ____

maximum displacement

When you suck on a straw, you expand your lungs, which reduces the air pressure inside your mouth to less than atmospheric pressure. Then the atmospheric pressure pushing on the liquid in the glass provides a ____ on the liquid in the straw sufficient to push the liquid up the straw.

net upward force

The people are moving up and down, and the wave is traveling around the stadium. Thus, the motion of the wave is perpendicular to the oscillation direction of the people, and so this is a ____.

transverse wave

What distance would reduce the intensity by a factor of 100?

twenty units less?

Because density is defined as ρ = M/V, the ____ matters as well. Thus, it could be simply that the first material has a more compact arrangement of molecules, such that there are more molecules in a given volume, which would lead to a higher density.

volume

All wave types—transverse,longitudinal, surface—have all of these five properties:

wavelength, frequency, amplitude, velocity, and period.

increase by 10 dB increase intensity by factor of ___ increase by 20 dB increase intensity by factor of ___ increase by 30 dB increase intensity by factor of ____

10^1 (10) 10^2 (100) 10^3 (1000)

In the open pipe, __ of a wave "fits" into the pipe, and in the closed pipe, only ___ of a wave fits. Because the wavelength is larger in the closed pipe, the frequency will be lower.

1/2; 1/4

An object floats in water with ¾ of its volume submerged. What is the ratio of the density of the object to that of water? a) 1/4 b) 1/3 c) 4/3 d) 3/4 e) 2/1

3/4

We know that v = fλ = λ / T, hence T = λ / v. If λ = 20 m and v = 5 m/s, then T =___ secs. The time to go from a crest to a trough is only____, so it takes 2 seconds!

4; T/2 (half a period)

Recall that a difference of 10 dB in intensity level b corresponds to a factor of 101 in intensity. Similarly, a difference of 60 dB in β corresponds to a factor of 106 in intensity. In this case, with two voices adding up, the intensity increases by only a factor of 2, meaning that the intensity level is higher by an amount equal toΔβ = 10 log(2) = 3 dB. The new intensity level is β =

63 dB.

What type of wave occurs when you toss a pebble in a pond?

A transverse wave

A quiet radio has an intensity level of about 40 dB. Busy street traffic has a level of about 70 dB. How much greater is the intensity of the street traffic compared to the radio? a) About the same b) About 10 times c) About 100 times d) About 1000 times e) About 10,000 times

About 1000 times

You hear a fire truck with a certain intensity, and you are about 1 mile away. Another person hears the same fire truck with an intensity that is about 10 times less. Roughly, how far is the other person from the fire truck? a) About the same distance b) About 3 miles c) About 10 miles d) About 30 miles e) About 100 miles

About 3 miles

When you drink liquid through a straw, which of the following is primarily responsible? a) Water pressure b) Gravity c) Inertia d) Atmospheric pressure e) Mass

Atmospheric pressure

When Mary talks, she creates an intensity level of 60 dB at your location. Alice talks with the same volume, also giving 60 dB at your location. If both Mary and Alice talk simultaneously from the same spot, what would be the new intensity level that you hear? a) More than 120 dB b) 120 dB c) Between 60 dB and 120 dB d) 60 dB e) Less than 60 dB

Between 60 dB and 120 dB

You stand a certain distance away from a speaker and you hear a certain intensity of sound. If you double your distance from the speaker, what happens to the sound intensity at your new position? a) Drops to ½ its original value b) Drops to ¼ its original value c) Drops to 1/8 its original value d) Drops to 1/16 its original value e) Does not change at all

Drops 1/4 its original value

Two drinking glasses, 1 and 2, are filled with water to the same depth. Glass 1 has twice the diameter of glass 2. Is the pressure at the bottom of glass 1 greater than, less than, or equal to the pressure at the bottom of glass 2?

Equal to

Water flows through a horizontal tube of diameter 2.7 cm that is joined to a second horizontal tube of diameter 2.0 cm. The pressure difference between the tubes is 7.6 kPa. Which tube has the higher pressure?

First tube

If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change? a) Frequency will increase b) Frequency will not change c) Frequency will decrease

Frequency will decrease

A wood whistle has a variable length. You just heard the tone from the whistle at maximum length. If the air column is made shorter by moving the end stop, what happens to the frequency? a) Frequency will increase b) Frequency will not change c) Frequency will decrease

Frequency will increase

Two drinking glasses, 1 and 2, are filled with water to the same depth. Glass 1 has twice the diameter of glass 2. Is the weight of the water in glass 1 greater than, less than, or equal to the weight of the water in glass 2?

Greater than

Why is the speed of sound greater in helium than in air?

Helium is significantly less dense than air.

In the previous question, the horn had a rest frequency of f0, and we found that your friend heard a higher frequency f1 due to the Doppler shift. The sound from the boat hits the cliff behind your friend and returns to you as an echo. What is the frequency of the echo that you hear? a) Lower than f0 b) Equal to f0 c) Higher than f0 but lower than f1 d) Equal to f1 e) Higher than f1

Higher than f1

You are heading toward an island in a speedboat and you see your friend standing on the shore, at the base of a cliff. You sound the boat's horn to alert your friend of your arrival. If the horn has a rest frequency of f0, what frequency does your friend hear? a) Lower than f0 b) Equal to f0 c) Higher than f0

Higher that f0

In order for b to be equal to zero, the term log(I/I0) must also be zero. This occurs when the argument is 1.0, because log(1.0) = 0. In other words, the value of I must be equal to ___.

I0

Speakers A and B emit sound waves of λ = 1 m, which interfere constructively at a donkey located far away (say, 200 m). What happens to the sound intensity if speaker A steps back 2.5 m? a) Intensity increases b) Intensity stays the same c) Intensity goes to zero d) Impossible to tell

Intensity goes to zero

Intensity level is given by β = 10 log(I/I0) with I0 = 10−12 W/m2. The usual threshold of human hearing is defined as an intensity level of β = 0 dB. What does this actually mean in terms of sound intensity? a) Intensity is undefined at that level. b) Intensity is 10^0 W/m2. c) Intensity is 0.0 W/m2. d) Intensity is 10^−12 W/m2. e) Intensity is 1.0 W/m2

Intensity is 10^−12 W/m2.

You put a straw into a glass of water, place your finger over the top so no air can get in or out, and then lift the straw from the liquid. You find that the straw retains some liquid. How does the air pressure P in the upper part compare to atmospheric pressure PA? a) Greater than PA b) Equal to PA c) Less than PA

Less than PA

Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day? a) More quickly on a hot day b) Equal times on both days c) More quickly on a cold day

More quickly on a hot day

If one material has a higher density than another, does this mean that the molecules of the first material must be more massive than those of the second?

No

The traces below show beats that occur when two different pairs of waves interfere. For which case is the difference in frequency of the original waves greater ? (One is three short squiggles, the other is two, thick and long squiggles) a) Pair 1 b) Pair 2 c) Same for both pairs d) Impossible to tell by just looking

Pair 1

Water flows through a horizontal tube of diameter 2.7 cm that is joined to a second horizontal tube of diameter 2.0 cm. The pressure difference between the tubes is 7.6 kPa. Which tube has the higher speed of flow?

Second tube

You have a long pipe and a short pipe. Which one has the higher frequency? a) The long pipe b) The short pipe c) Both have the same frequency d) Depends on the speed of sound in the pipe

Short pipe

A wave pulse is sent down a rope of a certain thickness and a certain tension. A second rope made of the same material is twice as thick, but is held at the same tension. How will the wave speed in the second rope compare to that of the first? a) Speed increases b) Speed does not change c) Speed decreases

Speed decreases

A length of rope L and mass M hangs from a ceiling. If the bottom of the rope is jerked sharply, a wave pulse will travel up the rope. As the wave travels upward, what happens to its speed? Keep in mind that the rope is not massless. a) Speed increases b) Speed does not change c) Speed decreases

Speed increases

A wave pulse can be sent down a rope by jerking sharply on the free end. If the tension of the rope is increased, how will that affect the speed of the wave? a) Speed increases b) Speed does not change c) Speed decreases

Speed increases

When a hole is made in the side of a cola can holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow will a) diminish. b) stop altogether. c) go out in a straight line. d) curve upward.

Stop all together

The vertical displacement of a wave on a string is described by the equation y(x,t)=Asin(Bx−Ct)y(x,t)=Asin⁡(Bx−Ct), in which AA, BB, and CC are positive constants. Does this wave propagate in the positive or negative x direction?

The positive x direction

Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured? a) The pressure on your skin b) The net applied force on your skin c) Both pressure and net applied force are equivalent d) Neither pressure nor net applied force are relevant here.

The pressure on your skin

Imagine holding two identical bricks in place underwater. Brick 1 is just beneath the surface of the water, and brick 2 is held about 2 feet down. The force needed to hold brick 2 in place is a) greater. b) the same. c) smaller.

The same

If you fill your lungs with helium and then try talking, you sound like Donald Duck. What conclusion can you reach about the speed of sound in helium? a) Speed of sound is less in helium b) Speed of sound is the same in helium c) Speed of sound is greater in helium d) This effect has nothing to do with the speed in helium.

The speed of sound is greater in helium

At a football game, the "wave" might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as? a) Polarized wave b) Longitudinal wave c) Lateral wave d) Transverse wave e) Soliton wave

Transverse Wave

A boat is moored in a fixed location, and waves make it move up and down. If the spacing between wave crests is 20 m, and the speed of the waves is 5 m/s, how long does it take the boat to go from the top of a crest to the bottom of a trough? a) 1 second b) 2 seconds c) 4 seconds d) 8 seconds e) 16 seconds

Two seconds

a) Remember that we have: ____ b) so if the ratio of the volume of the displaced water to the volume of the object is 3/4, the object has the density of water.

Vfluid/Vobject = Pobject/Pfluid

Does a longitudinal wave, such as a sound wave, have an amplitude? a) Yes b) No c) It depends on the medium the wave is in.

Yes

You blow into an open pipe and produce a tone. What happens to the frequency of the tone if you close the end of the pipe and blow into it again? a) Depends on the speed of sound in the pipe b) You hear the same frequency c) You hear a higher frequency d) You hear a lower frequency

You hear a lower frequency

Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled A? (normal wave chart going to the right) a) east b) southeast c) south d) north e) zero

Zero

The sound wave bouncing off the cliff has the same frequency f1 as the one hitting the cliff (what your friend hears). For the echo, you are now a moving observer approaching the sound wave of frequency f1, so you will hear ____

an even higher frequency.

Two bicycles approach one another, each traveling with a speed of 9.00 m/sm/s . Bicyclist A beeps it's horn. Which of the following would cause the greater increase in the frequency heard by bicyclist B: (i) Bicyclist A speeds up by 1.50 m/sm/s, or (ii) bicyclist B speeds up by 1.5 m/sm/s?

bicyclist A speeding up will have the greatest effect

Is the beat frequency produced when a 245 Hz tone and a 240 Hz tone are played together greater than, less than, or equal to the beat frequency produced when a 140-Hz tone and a 145-Hz tone are played together?

equal to

In the case of the pin vs pen; the net force is the same in both cases. However, in the case of the pin, that force is concentrated over a much smaller area of contact with the skin, such that the pressure is much greater. Because the ____ is greater, the pin is more likely to puncture the skin.

force per unit area

The higher pitch implies a higher ___. In turn, because v = fλ, this means that the speed of the wave has ___ (as long as the wavelength, determined by the length of the vocal chords, remains constant).

frequency; increased

Recall that the beat frequency is the difference in frequency between the two waves: fbeat = f2 - f1. Pair 1 has more oscillations in same time period, so pair 1 has____ and ____

greater beat frequency; the greater frequency difference.

Two strings are made of the same material and have waves of equal speed. String 1 is thick; string 2 is thin. Is the tension in string 1 greater than, less than, or equal to the tension in string 2?

greater than the tension in string 2

Due to the approach of the source toward the stationary observer, the frequency is shifted ____.

higher

A shorter pipe means that the standing wave in the pipe would have a shorter wavelength. Because the wave speed remains the same, and we know that v = fλ, then we see that the frequency has to ___ when the pipe is made shorter.

increase

The tension in the rope is ____ in the case of a massive rope. The tension ____ as you move up higher along the rope, because that part of the rope has to support all of the mass below it. Because the of this, the wave speed ____

not constant; increases; also increases

For a source of a given power P, the intensity is given by I = P/4πr2. So if the distance doubles, the intensity must decrease to ___ its original value.

one-quarter

The speed of sound in a gas increases with temperature. This is because the molecules are bumping into each other faster and more often, so it is easier to ____

propagate the compression wave (sound wave).

String 1 must have a greater ___ to compensate for its greater mass per length

tension

The wave speed depends on the square root of the ____, so if that increases, then the wave speed will also increase.

tension

a) Consider the forces acting at the bottom of the straw: PA - P - ρgH = 0 b) This point is in equilibrium, so net force is zero. c) Thus, P = PA - ρgH and so we see that ____

the pressure P inside the straw must be less than the outside pressure PA.

The force needed to hold the brick in place underwater is W - FB. According to Archimedes' principle, FB is equal to the weight of the fluid displaced. Because each brick displaces ____ of fluid, then FB is ____

the same amount; the same in both cases.

Water flows out of the hole because the water pressure inside is larger than the air pressure outside. The water pressure is due to the ____. When the can is in free fall, the water is weightless, so the water pressure is zero, and hence no water is pushed out of the hole

weight of the water

What is the smallest positive value of xxx where the displacement of this wave is zero at t=0?

x smallest= pi/B