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college physics reasoning

College Physics Reasoning and Relationships 2nd edition Nicholas Giordano - Solutions

You are at a rock concert and find that when you stand 10 m from a speaker, the intensity is so high that it hurts your ears. You decide to move away from the stage so that your ears are more comfortable. If you want to reduce the intensity at your ears by a factor of three, how far from the
The intensity of sunlight at the Earth?s surface is about 1000 W/m2. What is the intensity of sunlight at the surface of Saturn? From Table 5.1, the distance from the Sun to the Earth is 1.50 ? 1011 m, and the distance from the Sun to Saturn is 14.3 ? 1011 m. ? TABLE 5.1 Solar System Data:
Two waves of equal frequency are traveling in opposite directions on a string. Constructive interference is found at two spots on the string that are separated by a distance of 1.5 m.(a) What is the longest possible wavelength of the waves?(b) Give two other possible values of the wavelength.
Figure P12.40 shows an experiment in which sound waves generated by a singer and having a single frequency are emitted by two speakers. These sound waves interfere at a listener located at point P. If the interference at P is constructive, what is a possible value of the frequency? Figure P12.40 ?
Identical sound waves of frequency f are emitted from speakers at points A and B (Fig. P12.41), which are a distance 8.5 m apart. Listeners are located at points X, Y, and Z, which are equally spaced on the line between A and B. One listener finds constructive interference of the sound waves, and
Consider a radar system in an air traffic control center that is monitoring the distance to an approaching airplane. If the airplane is 4.0 km from the control center, what is the time delay between a transmitted wave pulse and the return of the reflected pulse?
Sonar is a system similar to radar except that sound is used in place of radio waves. Sonar systems are generally operated under water, where the speed of sound is approximately 1500 m/s. Suppose you are on a ship monitoring the distance to a submarine using sonar, and you find that the sonar
A radar system can measure the time delay between the transmitted and reflected wave pulses from a distant airplane with an accuracy of 1.0 picosecond. What is the accuracy in the calculated distance to the plane?
When sound waves are studied deep within the ocean, it is found that a plane wave that is initially parallel to the ocean floor will gradually bend upward and have a propagation direction that is tilted slightly toward the surface (Fig. P12.45). Does the speed of sound at these depths increase or
What is the distance between two nodes of a standing wave?(a) λ/4 (b) λ/2 (c) λ (d) 2λ (e) 3λ/2 (f) 3λ (g) Choices (c), (d), and (f) (h) Choices (b) and (e)
What is the distance between a node and an antinode of a standing wave?(a) λ/4 (b) λ/2 (c) λ (d) 2λ (e) 3λ/2 (f) 3λ (g) Choices (c), (d), and (f) (h) Choices (b) and (e)
The anti node of a standing wave is 0.057 m away from the nearest node. What is the wavelength of the waves that combine to make the standing wave?
Consider a guitar string that has a tension of 90 N, a length of 65 cm, and a mass per unit length of 7.9 × 10–4 kg/m. What is the fundamental frequency of the string? That is, what is the frequency of the standing wave with the lowest possible frequency? What note does this string emit when
You are studying guitar strings and are able to measure a few (but not all) of the standing wave frequencies for a particular string. If you measure frequencies of 450 Hz, 750 Hz, 900 Hz, and 1200 Hz, what is the highest possible value for the fundamental frequency?
A violin string is 35 cm long and has a fundamental standing wave frequency of 440 Hz. If the tension is 75 N, what is the mass of the string?
A vibrating string has a fundamental frequency of 250 Hz. The tension is then increased by a factor of 1.9. What is the new value of the fundamental frequency?
A violin string has an initial tension of 45.0 N. When playing the note A on the violin, the frequency is found to be 435 Hz. This note should actually have the frequency 440 Hz, so the player increases the tension to get the correct frequency. What is the new value of the tension? Give your answer
A steel piano string for the note middle C is about 0.60 m long and is under a tension of 600 N. If the fundamental frequency is 262 Hz, what is the string’s diameter?
The vibrating length of a guitar string is reduced by a factor of 2.5 when a player holds the string against a fret. What is the change in the frequency of the fundamental standing wave on the string?
Two nearby nodes of a standing wave are separated by 3.5 m. If the frequency of the wave is 150 Hz, what is the speed of the wave?
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 is the ratio of the lengths of the strings?
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 made of the same material and have the same diameter and tension, what is the ratio of the lengths of
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 minutes and 35 seconds later. If the speed of the P wave is 6.0 km/s and the speed of the S wave is 3.5
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 waves travel in a straight line to New York City.
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 and return. If the steel cable is 3.8 cm in diameter, what is the tension in the cable?
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 propagates from the end at a velocity of 15 m/s. (a) The wave pulse crosses over the weld and onto the
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 the points, from highest to lowest, according to the average vertical speed of each point during the
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 “drop-D” tuning, where the low E string is tuned so that it plays the note D instead. What decrease
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 stretched between the two homes at a tension of 10 N over the distance of 35 m. (a) How long does it
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 the soil in that area is 3.1 g/cm3. How long after the P waves have shaken the home does the sound
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 tuning.? (a) If the strings are made of a steel alloy of density ? = 6.3 g/cm3, what is the total force on the
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 aluminum with a steel core added for strength. The cross sectional areas of the steel and aluminum in
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 shows a different set of two pulses. Sketch the resulting waveform for these pulses at the times t =
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 tune all four strings of the violin to the same tension. A typical violin string tension is about 45 N,
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 from the surface. The speed of light in air depends on the air temperature, and this variation of the
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 ?stiffness.? According to this measure, order the materials in the table from least stiff to most
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 horizontal direction or (b) in a vertical direction? Figure Q12.10 ? تو
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 more slowly than both P and S waves. Even if all these waves had the same velocities, however, the
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 why.
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 Earth to the Sun.
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 the speed of the wave? Explain. Figure P12.6 ? y 20 - x (m) 30 10
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 particular string can be used to play notes with different frequencies. The frequency of a note is
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 travels up the rope. Does it change? Why or why not? Is the tension the same at all points on the string?
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 explosion rattles her window. The next day, she reads that an underground munitions dump exploded about 10
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 speed(d) The wavelength
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 B? Figure P12.15 ? y AA- A В 2 3
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 waves gives a standing wave. That is, show that this sum has nodes and anti nodes as sketched in the
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 = 1.5 s.
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 value of p? Figure 12.11
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 function of time. Show two complete periods of the wave.
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 strings of the same diameter. Will the tension in the steel strings be greater or less than in the
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. Assume the density is the same as that of steel, 7800 kg/m3.
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 × 420 kg/m3, what is the speed of sound in spruce? How does that compare with the speed of sound in
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) Sound waves in a room(b) Waves on a guitar string(c) Seismic waves in the Earth(d) Waves on the
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 velocity of the wave? 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
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) Seismic waves in the Earth
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 40 50 60 70 -0.2 30 20
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) 10 20 30 40 50 60 70 -0.2 _t = 2 s 0.2 x (m) 10 20 30 40 50 60 70 -0.2 30 20
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 P9.76 ? h = 3.0 cm
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 her initial kinetic energy?? Figure 9.11 ? wi Wf L; = I;w; = Ifwf=L¡ %3D Smaller than I; Larger
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 spherical shell, (c) a solid cylinder, or (d) a solid sphere?
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 and (b) The ratio of the total kinetic energy 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 velocity of the turbine is also proportional to the wind speed.? (a) Show that the mechanical power exerted
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? during flight. Cabin pressure, however, is lower than the pressure at sea level. Cabins typically
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 = cross-sectional area - Lo- Ax F This end is held fixed.
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 change in diameter is small, so keep at least four significant figures in your calculation.
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. What is the change in length of the bone?(b) If the bone has a diameter of 3 cm, how much weight
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→

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