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college physics reasoning

Questions and Answers of College Physics Reasoning

Consider a standing wave that has a frequency of 2000 Hz and a speed of 300 m/s. What is the distance between a node and the nearest anti node?
Figure P12.58 shows a standing wave on a string. If the frequency of the wave is 440 Hz, what is the speed of a wave on this string? Figure P12.58 ? 0.60 m
You want to set up a standing wave on a string that has a length of 3.5 m. You find that the lowest frequency that will work is 20 Hz. What is the speed of a wave on this string?
Two notes on a guitar that differ by an octave have fundamental frequencies that differ by a factor of exactly two. If these notes are played on strings that have the same diameter and tension, what
Consider two notes on a guitar whose fundamental frequencies are in the ratio 5/4. These notes differ by a musical interval called a “major third.” If these notes are played on strings that are
You are operating a seismic laboratory when an earthquake occurs. Your seismographs indicate that the P wave generated by the earthquake arrives at precisely 1:55 PM, whereas the S wave arrives 5
An earthquake occurs at the South Pole. If the speed of the P waves is 6.0 km/s and the speed of the surface waves is 2.2 km/s, how long will it take these waves to reach New York City? Assume the
A lift mechanic taps on an end of the main cable of a ski lift 2000 ft (610 m) long, sending a transverse pulse down the cable. He finds it takes 7.7 s for the pulse to reflect off the opposite end
Two cables of equal diameter and length, one made of aluminum and the other made of steel, are welded together and strung horizontally under tension. When the aluminum end is struck, a wave pulse
A wave pulse moves along a strip of rubber with a velocity of 10 cm/s as depicted in Figure P12.66. Five equally spaced points are marked on the rubber strip labeled A though E as shown.? (a) Rank
A guitar string that should produce 110 Hz (the note A) instead produces 105 Hz. (a) What change in tension is needed to bring the string into tune? (b) Sometimes a guitar is tuned to
Two neighbors communicate with a homemade string phone (Fig. P12.68). The simple phone consists of two ends of a string (total mass of 18 g) attached to the bottom of two paper cups. The string is
An explosion takes place in an underground mine 15 km away from a home located in a valley where the soil consists of a clay material with Young’s modulus Y = 2.9 × 109 Pa. The average density of
A standard guitar is strung with six strings of increasing diameter and all of length 65 cm. Each string is to have the fundamental frequency of the notes E, B, G, D, A, amd E for standard
In moderate winds, high-tension power lines sometimes ?sing? or hum as a result of transverse waves on the lines that winds can generate. The cables that carry high-voltage electricity are made of
Figure P12.72A shows two wave pulses at time t = 0 s. The pulses travel at 5 cm/s in opposite directions.? (a) Sketch the resulting waveform for the times t = 1 s, 2 s, and 3 s.? (b) Figure P12.72B
Wolfgang Mozart was not only an outstanding composer, but also an excellent violinist. His violin teacher was his father, Leopold, and historical records show that Leopold advised his students to
A mirage is created by refraction of light near the surface of the Earth. On a still day (no wind), absorption of sunlight by the Earth makes the air temperature decrease as one moves upward, away
Table P12.75 lists the speed of sound and the density of diamond (a crystal composed of carbon) and several metals. Some authors use the Young?s modulus of a material as a measure of the material?s
Figure Q12.10 shows a child holding one end of a long Slinky. If the child wants to generate a longitudinal wave in the Slinky, in what direction should he shake the end of the Slinky, (a) in a
A wave on a string is described by the equation y = (4.2 mm cos(3000t - 0.45x) where t is measured in s and x is measured in mm. What are the frequency and wavelength of the wave?
Seismic waves in the Earth. Surface seismic waves generated by an earthquake arrive at a distant observer after the arrival of P waves and S waves (Fig. 12.27B), partly because surface waves travel
The speed of longitudinal waves in a metal is 3000 m/s. If the density is 12,000 kg/m3, what is the Young’s modulus of the metal?
For guitars and violins, some strings are “simple” strings, and others contain a winding around a string core. Which type of string, simple or wound, is used for the low-frequency notes? Explain
Waves on a violin string travel at 900 m/s. If the string has a tension of 50 N and is 0.33 m long, what is its mass?
In a sound wave in a solid, the atoms in the solid move parallel to the propagation direction. Does that means the atoms travel along with the wave? Explain why or why not.
A rough rule of thumb is that light from the Sun reaches the Earth in about 8 minutes. Use this estimate along with the known speed of light to get an approximate value for the distance from the
A key property of a wave is that it transports energy without transporting mass. Explain how this is possible, using work– energy ideas (i.e., W = F Δx). Consider the “leading edge” of a wave.
Figure P12.6 shows a snapshot of a portion of a periodic wave as it travels along a string. Estimate the wavelength of the wave. Is there enough information in this figure for you to also estimate
Devise or describe an experiment that uses standing waves to measure the velocity of a wave.
Figure P12.7 shows a snapshot of a wave on a string. If the frequency of this wave is 20 Hz, what is the approximate speed of the wave? Figure P12.7 ? y х (ст) 1 2 3
A bass guitar has longer strings than a regular guitar. Explain why these longer strings allow a bass guitarist to play “lower” notes.
A wave on a Slinky has a frequency of 2.3 Hz. It takes 3.5 s to travel the length of the Slinky (0.30 m). What is the wavelength?
The neck of a guitar is designed with frets as shown in Figure Q12.8. A player can hold a string against one of the frets and thus shorten the vibrating length L of the string. In this way, a
Sound waves in water travel at a speed of approximately 1500 m/s. What is the wavelength of a sound wave that has a frequency of 440 Hz?
Important properties of a wave on a string include the (a) wavelength, (b) frequency, (c) amplitude, and (d) speed. Which of these properties is independent of the others? Explain.
A wave on a string is described by the relation y = A sin(35t - 0.025x), where t is measured in seconds and x in meters, with A = 0.15 m. Find the frequency, wavelength, and speed of this wave.
A wave on a string is described by the relation y = A sin(72t - 0.045x), where t is measured in seconds and x in meters, with A = 0.15 m. What is the maximum speed of a point on the string?
Using Equation 12.1, write the equation of a wave on a string that has an amplitude of 0.30 m, a frequency of 350 Hz, and a velocity of 250 m/s and travels to the right.
A rope of linear density of about 1 kg per meter is hung from the ceiling. The lower free end is then oscillated, producing waves that travel up the rope. Describe the velocity of the wave as it
Using Equation 12.1, write the equation of a wave on a string that has an amplitude of 0.50 m, a wavelength of 8.4 m, and a velocity of 330 m/s and travels to the left.
A woman wakes up just after 2 AM. Wondering what woke her, she goes to the window and looks around. Noting nothing out of the ordinary, she sits back down on her bed and all of a sudden a loud
When a sound wave passes from air into a solid object, which of the following wave properties stays the same and which change?Explain.(a) The amplitude (b) The frequency (c) The wave
Figure P12.15 shows a snapshot of a wave on a string. This wave has a frequency of 200 Hz. Approximately how long does it take the wave crest located at point A in this snapshot to move to point
Equation 12.1 describes a wave that is traveling to the right, and Equation 12.5 corresponds to a wave of the same frequency and wavelength that is moving to the left. Show that the sum of these two
Draw a snapshot of a wave on a string that obeys the equation y = (4.2 mm)cos(3000t - 0.45x). Assume the units of length are millimeters and the units of time are seconds. Make your drawing at t =
Consider a water wave as illustrated in Figure 12.11. This wave front is circular. How does the intensity of this wave vary as it moves away from its source? You should find that I ? rp. What is the
Which property of a wave is independent of its amplitude, (a) frequency, (b) wavelength, or (c) speed?
A wave on a string is described by the equation y = (4.2 mm cos(3000t - 0.45x), where t is measured in s and x is measured in mm. Make a graph of the displacement of the string at x = 0.35 mm as a
Most modern guitars use steel strings, whereas many historical instruments use strings made of animal gut. Suppose the strings on a guitar that was originally strung with gut are replaced with steel
Consider a wave that has a frequency of 3.0 kHz and a wavelength of 0.10 m. What is the speed of this wave?
When you tune a guitar, what causes the frequency to change?
Two sound waves in air have frequencies that differ by a factor of five. What is the ratio of their wavelengths?
A wave on a string has a speed of 340 m/s. If the tension in the string is 150 N and its length is 2.0 m, what is the mass of the string?
Consider a piano string made of steel with a diameter of 1.0 mm. If the speed of a wave on this string is 280 m/s, what is the tension in the string? The density of steel is 7800 kg/m3.
A wave on a string has a speed of 200 m/s. If the diameter of the string is increased by a factor of two and the tension is held fixed, what is the speed of the wave on this new string?
Consider a violin string with a vibrating length of 30 cm. If the speed of a wave on this string is 250 m/s, what is the tension in the string? You will have to estimate the diameter of the string.
The speed of a wave on a guitar string is v = 120 m/s. If the tension is increased from 70 N to 110 N, what is the new value of v?
The speed of sound in water is 1500 m/s. Find the wavelength of a sound wave whose frequency is 300 Hz.
Spruce is a type of wood that is widely used in making musical instruments (such as violins and guitars) because its Young’s modulus is high and its density is low. If Y = 1.5 × 1010 Pa and ρ ×
Consider the speed of sound in a hypothetical metal. If the density is reduced by a factor of three and all other properties are unchanged, by what factor is the speed of sound changed?
Consider a clothesline stretched between two supports. If one end of the line is “wiggled,” a wave will be produced. Estimate the speed of this wave on a clothesline.
Identify the following waves as either longitudinal or transverse or both. Use a drawing to illustrate how the motion of the wave’s medium is related to the direction of propagation of the wave.(a)
For the wave in Figure P12.1, what is the approximate magnitude of the speed of a section of the string as the wave pulse passes by? What is the direction of the string velocity relative to the
Identify the medium for each of the following waves:(a) Sound waves in a room(b) Waves on the surface of a pond(c) Radio waves(d) Light waves(e) Waves created when a guitar string is plucked(f)
Is the wave on a string in Figure P12.1 transverse or longitudinal? Figure P12.1 ? у (m) t = 0 0.2 x (m) 10 40 50 60 70 -0.2 0.2 _t = 1 s x (m) 10 20 30 40 50 60 70 -0.2 _t = 2 s 0.2 x (m) 10 20 30
Figure P12.1 shows several snapshots of a wave pulse as it travels along a string. Estimate the speed of the wave pulse. Figure P12.1 ? у (m) t = 0 0.2 x (m) 10 40 50 60 70 -0.2 0.2 _t = 1 s x (m)
Estimate the kinetic energy of the spinning top in Figure P9.76. Assume it is made of wood and is rotating with ? = 30 rad/s. You will need to estimate the radius of the top from the figure.? Figure
A figure skater (Fig. 9.11) has an initial angular velocity of 3.8 rad/s. She then pulls her arms in, and her angular velocity increases to 9.5 rad/s. What is the ratio of her final kinetic energy to
An object is rolling without slipping, with a transnational kinetic energy of KEtrans and a rotational kinetic energy of KErot. If KEtrans / KErot = 3/2, what might this object be, (a) a hoop, (b) a
A solid sphere and a solid cylinder, both of mass m and radius R, are rolling without slipping with speed v. Find (a) The ratio of the angular momentum of the sphere to that of the cylinder
Electrical power produced by a wind turbine. The force of the wind on the blades of a wind turbine (Fig. 9.4A) is proportional to v2, where v is the speed of the wind (Chapter 3). The angular
The density of air decreases with height above the Earth, and when the density is too low, people get sick or even become unconscious. That is why the cabins of commercial airplanes are ?pressurized?
A thick copper wire of length 10 m is observed to stretch 0.10 cm. What is the strain? If the applied force is 50,000 N, what is the diameter of the wire?
A shear force of 3.0 ? 105 N is applied to an aluminum bar of length L = 20 cm, width w = 5.0 cm, and height h = 2.0 cm as shown in Figure 11.23. What is the shear deformation??x? Figure 11.23 ? A =
A solid glass sphere with an initial diameter d = 25.00 cm is subject to a pressure of 1000 × Patm, where atmospheric pressure Patm = 1.01 × 105 Pa. What is the new diameter of the sphere? The
If the frequency of a wave is doubled, how does the wavelength change?
A guitar string of diameter 0.50 mm and length 0.75 m is subject to a tension of 150 N. If the string stretches an amount 0.40 mm, what is Young’s modulus of the string?
Young’s modulus for bone under compression is about 9 × 109 Pa, and the breaking stress is about 2 × 108 Pa. (a) A leg bone of length 30 cm when unstressed is stressed to its breaking point.
A steel cylinder of length 11 cm and radius R = 3.5 cm (Fig. P11.53A) is subjected to a compressive force of 5000 N. By what amount??L is the cylinder compressed? Figure P11.53A ? R F F -L→
The steel cylinder in Figure P11.53A is replaced by a steel tube (Fig. P11.53B). The outer radius of the tube is R1 = 3.5 cm, and the inner radius is R2 = 1.5 cm. If the compressive force is F = 5000
Two bars, one composed of aluminum and one of steel, are placed end to end as shown in Figure P11.56. The bars are both initially of length L = 25 cm, and both have a square cross section with h =
An aluminum sphere has a radius of 45 cm on the Earth. It is then taken to a distant planet where the atmospheric pressure P is much larger than on the Earth. If the sphere has a radius of 43 cm on
You want to use a steel cable to tow your car (m = 2000 kg). The cable is solid steel with a diameter of 1.0 cm and a length of 10 m. If you are pulling the car such that its acceleration is 1.5
A steel string (diameter 1.0 mm) of length 2.5 m hangs vertically. At the bottom of the string is a seat. When a child of mass m sits on the seat, she finds that the string stretches so that its new
A damped harmonic oscillator is displaced from equilibrium and then released. The oscillator displacement as a function of time is shown in Figure P11.60. Is this oscillator under-damped or over
Figure P11.61 shows the displacement as a function of time for an under-damped harmonic oscillator. Estimate the fraction of the mechanical energy that is ?lost? to friction during one cycle. Figure
Figure P11.62 shows the amplitude as a function of frequency for a driven, damped oscillator. Estimate the resonant frequency. Figure P11.62 ? 500 1000 1500 Frequency (Hz) Amplitude (mm)
Consider a Cavendish apparatus that employs a torsion fiber with k = 1.0 × 10-8 N · m. Suppose the smallest twist angle that can be measured is θ = 2.0°. If the distance from one of the masses m1
Get new struts! A car with worn-out (under-damped) struts is observed driving over a dip in the road. The car bounces up and down a total of three times in a period of 5 seconds after hitting the
A mass of 5.0 kg slides down a friction less slope into a spring with spring constant k = 4.9 kN/m as depicted in Figure P11.65. (a) If the spring experiences a maximum compression of 20 cm,
A mass of 3.5 kg is attached to a spring with spring constant k = 70 N/m. It is then compressed by 49 cm from its equilibrium position (Fig. P11.67, top) and released. At exactly the same time, an
The bumper on a car is made of flexible plastic so that it will compress on impact and “cushion” the car’s occupants during a collision. Suppose a car of mass m = 1200 kg is traveling slowly
Bobble-head. A football bobble-head figure sits on your car dashboard. The 85-g head of the figure is attached to a spring with spring constant k = 21 N/m (Fig. P11.69). You are driving along a
A solid rubber ball of radius 10 cm is submerged to 8.0 m beneath the surface of a lake. (a) If the bulk modulus of the rubber compound is Brubber = 4.0 × 106 Pa, what is the diameter of the
Air spring. The elasticity and bulk modulus of air can be measured using an apparatus consisting of a vertical glass tube and a ball bearing that just fits in the inner diameter of the tube. A 110-g
Young’s modulus of granite is about 5.0 × 1010 Pa. Assuming the elastic limit of granite corresponds to a compression of 10%, estimate how tall a mountain would have to be for the granite at the
Two playground swings are side by side. The children using the swings notice that one of the swings (swing 1) has a period of exactly 4.5 s. They also find that when the first swing has completed 10
Two solid rods having the same length are made of the same material with circular cross sections. Rod 1 has radius r, and rod 2 has radius 2r. If a compressive force F is applied to both rods, their
Consider a steel rod of diameter 5.0 mm and length 3.5 m. If a compressive force of 5000 N is applied to each end, what is the change in the length of the rod?

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