Day 11, Physics 131

HW Problem 12-6

• In one hand you hold a 0.11-kg apple, in the other hand a 0.24-kg orange. The apple and orange are separated by 0.85 m.

• ? What is the force of gravity that (a) the orange exerts on the apple and (b) the apple exerts on the orange. ?

HW Problem 12-20

• The acceleration due to gravity on the Moon’s surface is known to be about one-sixth the acceleration due to gravity on the Earth.

• Given the radius of the Moon is roughly one-quarter that of the Earth, find the mass of the Moon in terms of the mass of the Earth.

HW Problem 12-34

• GPS Satellites orbit at an altitude of 2.0 x 107 m.• ? (a) Find the orbital period ?• ? (b) Find the orbital speed of such a satellite ?

HW Problem 12-72

• An astronaut exploring a distant solar system lands on an unnamed planet with a radius of 3860 km. When the astronaut jumps upward with an initial speed of 3.10 m/s, she rises to a height of 0.580 m.

• ? What is the mass of the planet ?

HW Problem 12-78

• Suppose a planet is discovered that has the same total mass as the Earth, but half its radius.

• ? (a) Without plugging in numbers, explain whether the acceleration due to gravity on this planet is more than, less than, or the same as the acceleration due to gravity on the Earth. ?

• ? (b) Calculate “g” on this planet. ?

HW Problem 13-10

• The position of a mass oscillating on a spring is given by x = (3.2 cm) cos [2t/(0.58 s)].

• ? (a) What is the period of this motion ?• ? (b) what is the first time the mass is at the

position x = 0 ?

HW Problem 13-27

• Given: A structural beam in a spacecraft vibrates with an amplitude of 0.25 mm at a rate of 110 vibrations per second.

• ? Find the maximum acceleration of the beam, as a multiple of g = 9.81 m/s2 ?

HW Problem 13-29

• The pistons in an internal combustion engine undergo a motion that is approximately simple harmonic.

• Assume the amplitude of motion is 3.5 cm and the engine runs at 1700 rev/min.

• ? (a) Find the maximum acceleration of the pistons ?

• ? (b) Find their maximum speed ?

HW Problem 13-39

• When a 0.50-kg mass is attached to a vertical spring, the spring stretches by 15 cm.

• ? How much mass must be attached to the spring to result in a 0.75-s period of oscillation ?

HW Problem 13-41

• Two people with a combined mass of 125 kg get into an old car with worn-out shock absorbers. This causes the springs to compress by 8.00 cm. When the car hits a bump in the road, it oscillates up and down with a period of 1.65 s.

• ? (a) Find the total load supported by the springs. ?

• ? (b) Find the mass of the car. ?

HW Problem 13-59

• Radio microphone dangles down from booth nearly to the ground.

• Microphone swings back and forth like a pendulum.

• Fan (probably a physics professor) uses watch (or smart phone) to determine that 10 complete oscillations take 60.0 s.

• ? How high above the field is the radio booth ?

HW Problem 13-100

• A Snowy Tree Cricket chirps at a rate that follows the expression N = T – 39, where N is the number of chirps in 13 seconds and T is the numerical value of the temperature in degrees Fahrenheit.

• ? If the temperature is increases by 10 degrees Fahrenheit, how many additional chirps are heard in a 13-s interval ?

Chapter 14, Waves

• Transverse waves• Longitudinal or compressive waves. Slinky

• v = / T = f• f = frequency• T = period

Waves on a string

• = mass / length, “mass density”• v = ( F / ) ½ F = tension on string• v = speed of wave on string

• Harmonic Wave Functions• Equation 14-4. See function of x and of t.

Producing Sound Waves

• Loudspeakers• Vibrations• Explosions

• Speed of sound in air at 20o C = 343 m/s for this course, except for lab 9 on next Wednesday.

• Speed of sound in solid material much faster.

Well

• “The well is 1.5 seconds deep.”• Assume vsound = 343 m/s

Human Ear is remarkable

• The range of human hearing extends from approximately 20 Hz to 20 000 Hz.

• Find the wavelengths of these extremes for a sound speed of 343 m/s.

Sound Energy and Intensity

• Intensity, I, defined as (1/A)(E/t) • Intensity in watts / m2

• .. So I is power / area and spreads spherically

Eardrum

• The area of a typical eardrum is about 5.0 x 10-5 m2.

• ? Calculate the sound power (energy per second) incident on an eardrum at (a) the threshold of hearing (10-12 W/m2) and (b) the threshold of pain (1 W/m2) ?

Decibels

• “Intensity Level of Sound” or “Sound level”• Defined as = (10 dB) log10(I/Io)

• Where Io is 1 x 10-12 W/m2

• Called “decibels” there’s an app for that!

• This is the only use of logarithms in the course, as trig is now handled by calculators.

Sound Intensity I vs Intensity

• Sound Intensities, I, add, subtract, etc. Units are Watts / m2.

• Intensity levels, , decibels, do not

Toadfish

• A toadfish makes use of resonance in a closed tube to produce very loud sounds. The sound level, , of this creature has been measured as high as 90 dB.

• ? (a) Calculate the intensity, I, of the sound wave emitted. ?

• ? (b) What is the sound level, , if three of these fish sound off at the same time ?

Short lesson: Logarithms

Study the handout!

Doppler Effect

Siren

• An observer drives slowly due west at 24.59 m/s while approaching an fire truck driving due east at 33.53 m/s.

• The fire truck is sounding its siren, whose frequency is 4.00 x 102 Hz.

• ? What is the frequency of the sound as heard by the observer ?

A Passing train

• An alert physics student stands beside the tracks as a train rolls slowly by. He notes that the frequency of the train whistle is 442 Hz when the train is approaching him and 441 Hz when the train is receding from him.

• ? What’s the speed of the train. ?

Destructive Interference

• Two loudspeakers are placed on a wall, directly above and below each other, 3.0 m apart. They are driven by the same source at a frequency of 4.50 x 102 Hz. An observer is in front of the speakers 8.0 m from the wall, at the same distance from each speaker.

• ? If the speed of sound is 345 m/s, what minimum vertical distance upward should the top speaker be moved to create destructive interference at point “O” ?

Ship

• The ship in the figure travels along a straight line parallel to the shore and 600 m from it. She ship’s radio receives simultaneous signals of the same frequency from antennas A and B. The signals interfere constructively at point C, which is equidistant from A and B. The signal goes through the first minimum at point D.

• ? Determine the wavelength of the radio waves ?

Standing Waves

• See page 479 for terrific pictures of standing waves. We will produce visible standing waves in the lab on next Wednesday.

• The node-to-node distance is ½ • The ends are nodes, between the nodes are

the antinodes.• Fundamental = first harmonic• First overtone = second harmonic

Steel wire in piano

• Steel wire in piano of length = 0.7000 m• Mass = 4.300 x 10-3 kg• f = 261.6 Hz• ? What Tension on wire ?

Crystal goblet

• Standing-wave vibrations are set up in a crystal goblet with four nodes and four antinodes equally spaced around the 20.0-cm circumference of its rim.

• ? If transverse waves move around the glass at 900 m/s, and opera singer would have to produce a high harmonic with what frequency in order to shatter the glass with a resonant vibration. ?

Stretched String

• A stretched string fixed at each end has a mass of 40.0 g and a length of 8.00 m. The tension in the string is 49.0 N.

• ? (a) Determine the positions of the nodes and antinodes for the third harmonic. ?

• ? (b) What is the vibration frequency for this harmonic ?

Vibrating Columns of Air I

• Standing Waves in a Column of Air Closed at One End Equations 14-14

• f1 = v/4L

• fn = nf1 = nv/4L, n=1,3,5

• n = 1/n = 4L/n

• See Figure 14-27. Wednesday’s Lab

Vibrating Columns of Air II

• Standing Waves in columns of air Closed at both ends

• f1 = v/2L

• fn = nf1 = nv/2L, n=1,2,3 Equations 14-15

• n = 1/n = 2L/n

Tunnel

• A tunnel under a river is 2.00 km long.• ? (a) At what frequencies can the air in the

runnel resonate .?• ? (b) Explain whether it would be good to

make a rule against blowing your car horn when you are in a tunnel. ?

Fundamental Vibration of a solid rod

• Baseball bat• Picture of a marimba bar