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physics
oscillations mechanical waves

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

The Tacoma Narrows Bridge, built across Puget Sound in Washington, formed a standing wave before it collapsed on November 7, 1940. As seen in the photo in Fig.(a) How many full wavelengths were between the two towers, which were spaced 2800 ft apart? (b) If the frequency of the vibrations was 0.20
Maintaining strong AM radio reception when driving under overpasses or through tunnels is often difficult. FM radio frequencies typically are not as affected as AM frequencies. (a) Using the frequency range for AM radio, 550 kHz to 1650 kHz, and FM radio, 88 MHz to 108 MHz, find the range of
Dave, a jet engine technician, is exposed to sound intensities of at 10.3 W/m2 (120 dB) at 30.4 m from a jet Figure.(a) What is the audible power produced by the jet engine? (b) Since the sound power produced by the engine remains constant and the sound propagates in all directions (spherically),
The speed of an automobile can be determined using the Doppler effect by sounding the horn.(a) An automobile’s horn produces a frequency of 765 Hz. How fast is the car traveling if a stationary microphone measures the horn’s frequency as 836 Hz at a temperature of 23.3°C?(b) What is the
1. Find the period of a wave whose frequency is 500 Hz. 2. Find the frequency of a wave whose period is 0.550 s.3. Find the velocity of a wave with wavelength 2.00 m and frequency 400Hz
(a) What is the frequency of a light wave with wavelength 5.00 x 10–7m and velocity 3.00 × 108 m / s?(b) Find the period of the wave.
1. What is the speed of a wave with frequency 3.50 Hz and wavelength 0.550 m?2. Find the wavelength of water waves with frequency 0.650 Hz and velocity 1.50 m/s.3. What is the wavelength of longitudinal waves in a coil spring with frequency 7.50 Hz and velocity 6.10 m/s?
A wave generator produces 20 pulses in 3.50 s.(a) What is its period?(b) What is its frequency?
1. Find the frequency of a wave produced by a generator that emits 30 pulses in 2.50 s.2. What is the wavelength of an electromagnetic wave with frequency 50.0 MHz?3. What is the frequency of an electromagnetic wave with a wavelength of 0.25 m?4. What is the wavelength in metres of an
Find the wavelength of a wave traveling at 2.68 x 106 with a period of 0.0125 s.
Find the wavelength of a wave traveling twice the speed of sound (speed of sound = 331 m/s) that is produced by an oscillator emitting 63 pulses every 8.3 x 10–6 min.
1 (a) Find the velocity of X rays emitted with wavelength 3.00 x 10–9 m and frequency 3.00 x 1018 Hz.(b) Find the period of the waves.2. Find the velocity of microwaves having wavelength 0.750 m and frequency 2.75 x 1010 Hz.
1. Find the speed of sound in m/s at 10°C at1 atm pressure in dry air.2. Find the speed of sound in m/s at 35°C at 1 atm pressure in dry air.3. Find the speed of sound in m/s at –23°C at 1 atm pressure in dry air.
1. How long will it take a sound to travel 21.0 m for the conditions of Problem 1?2. How long will it take a sound to travel through 7500 m of water at 25°C?3. A sound wave is transmitted through water from one submarine, is reflected off another submarine 15 km away, and returns to the sonar
A woman is swimming when she hears the underwater sound wave from an exploding ship across the harbor. She immediately lifts her head out of the water. The sound wave from the explosion propagating through the air reaches her 4.00 s later. How far away is the ship? Assume that the water temperature
1. A train traveling at a speed of 40 m/s approaches an observer at a station and sounds a 550-Hz whistle. What frequency will be heard by the observer? Assume that the sound velocity in air is 345 m/s.2. What frequency is heard by an observer who hears the 450-Hz siren on a police car traveling at
A jet airplane taxiing on the runway at 13.0 km/h is moving away from you. The engine produces a frequency of 660 Hz in –6.0°C air. What frequency do you hear?
1. While snorkeling you hear a dolphin’s sound as it approaches at 5.00 m/s. If the perceived frequency is 850 Hz, what is the actual frequency being emitted?2. Two construction workers stand 112 m apart. One strikes a steel beam with a hammer. How long does it take for the other to hear the
A crop duster airplane flies overhead at 44.7 m/s. The frequency of the sound is 605 Hz. (a) What do you perceive as the frequency as it approaches? Assume the velocity of sound in air is 345 m/s. (b) What frequency do you hear as the plane flies away and has accelerated to 55.0 m/s?
1. Two iron workers are on a project 72.0 m apart. To get the other’s attention, one worker strikes his lunch pail with his wrench. How long does it take the sound to travel through the air if the speed of sound under these conditions is 345 m/s?2. A construction worker 30.0 m above the ground
1. Find the length (in cm) of a pendulum with a period of 1.50 s.2. Find the length (in ft) of a pendulum with a period of 3.00 s.3. Find the period of a pendulum 1.25 m long.4. Find the period of a pendulum 2.00 ft long.5. Find the length (in in.) of a pendulum with a period of 2.25 s.6. Find the
1. Find the period of a pendulum 35.0 cm long.2. If you double the length of a pendulum, what happens to its period?3. If you double the period of a pendulum, what happens to its length?4. A grandfather clock has a 0.750-m pendulum. What is its period?5. A grandfather clock has a pendulum with
1. Find the period of a wave with frequency 355 kHz.2. Find the frequency of a wave with period 0.320 s.3. (a) What is the frequency of a light wave with wavelength 4.50 x 10–7 m and velocity 3.00 x 108 m/s?(b) Find the period of the wave.4. Find the speed of a wave with frequency 8.97 Hz and
1. What is the wavelength of an electromagnetic wave with frequency 65.5 MHz?2. Find the speed of sound in m/s at 85°C at 1 atm pressure in dry air.3. Find the speed of sound in m/s at –35°C at 1 atm pressure in dry air.4. How long will it take a sound wave to travel through 1450 m of water at
A car is traveling toward you at 95 km/h. The car horn produces a sound at frequency 4950 Hz.(a) What frequency do you hear? Assume that the sound velocity in air is 345 m/s.(b) What frequency do you hear if the car is traveling away from you?
What is the frequency of the sound waves being emitted from a train whistle while approaching at 45 m/s in air that is 11°C? The perceived frequency is 425 Hz.
The taillight on a car produces light with wavelength 5.00 x 10–7 m. What frequency do you observe when the car is departing at 24 m/s at 0°C?
1. A pendulum has a length of 0.450 m. What is its period?2. A pendulum has a period of 0.700 s. Find the length of the pendulum in inches.
1. Which of the following are methods of energy transfer?(a) Conduction(b) Radiation(c) Wave motion(d) None of the above2. The minimum distance between particles in a wave that have the same displacement and are moving in the same direction is called(a) The period.(b) The frequency.(c) The
1. Which of the following are electromagnetic waves?(a) Sound(b) Water waves(c) Radar waves(d) X rays(e) All of the above2. Explain the difference between interference and diffraction.3. Explain the difference between constructive and destructive interference.4. If waves did not exhibit the
1. Explain the difference between a wave and a pulse.2. Give an example of a pulse.3. What happens to the speed of sound when the temperature increases? Explain why this might happen.4. Explain how a seismograph works.5. How does the speed of sound differ in water and air? Explain the reason for
In your own words, explain the Doppler effect.
1. Distinguish between sympathetic and forced vibration.2. In your own words, explain resonance.3. State a reason that might explain why many stars appear to have their light shifted to the red (longer wavelength) part of the electromagnetic spectrum when viewed from the earth.4. Distinguish
Distinguish between sympathetic and forced vibration.
If the amplitude of a particle in SHM is doubled, how are (a) The total energy (b) The maximum speed affected?
When a wave pulse travels along a rope, what travels with the wave motion and what does not travel with the wave?
Can harmonic sound of any frequency be generated and heard from a violin string with a fixed tension? Explain.
If they have the same tension and length, will a thicker or a thinner guitar string sound higher in frequency? Why?
A child’s swing (a pendulum) has only one natural frequency, f1, yet it can be driven or pushed smoothly at frequencies of f1/2, f1/3, and 2f1. How is this possible?
By rubbing the circular lip of a wide, thin wine glass with a moist finger, you can make the glass “sing.” (Try it.) (a) What causes this? (b) What would happen to the frequency of the sound if you added water to the glass?
A tennis player uses a racket to bounce a ball up and down with a constant period. Is this a simple harmonic motion? Explain.
If a mass–spring system were taken to the Moon, would the period of the system change? How about the period of a pendulum taken to the Moon? Explain.
If you want to increase the frequency of vibration of a mass–spring system, would you increase or decrease the mass? Explain.
One simple harmonic motion is described by a sine function, y = A sin (wt), and another is described by a cosine function, y = A cos(wt). Discuss the differences in their initial position, velocity, and acceleration.
(a) At what position is the magnitude of the force on a mass in a mass–spring system minimum: (1) x = 0, (2) x = – A, or (3) x = + A? Why? (b) If m = 0.500 kg, k = 150 N/m, and A = 0.150 m, what are the magnitude of the force on the mass and the acceleration of the mass at, x = 0.050 m, and
(a) At what position is the speed of a mass in a mass–spring system maximum: (1) x = 0, (2) x = – A, or (3) x = + A? Why? (b) If m = 0.250 kg, k = 1000 N/m, and A = 0.10m for such a system, what is the mass’s maximum speed?
A mass–spring system is in SHM in the horizontal direction. If the mass is 0.25 kg, the spring constant is 12 N/m, and the amplitude is 15 cm, (a) What is the maximum speed of the mass, and (b) Where does this occur? (c) What is the speed at a half-amplitude position?
A horizontal spring on a frictionless level air track has a 0.150-kg object attached to it and it is stretched 6.50 cm. Then the object is given an outward initial velocity of 2.20 m/s. If the spring constant is 35.2 N/m, determine how much farther the spring stretches.
A 0.25-kg object is suspended on a light spring of spring constant 49 N/m. The spring is then compressed to a position 15 cm above the stretched equilibrium position. How much more energy does the system have at the compressed position than at the stretched equilibrium position?
A 0.25-kg object is suspended on a light spring of spring constant 49 N/m and the system is allowed to come to rest at its equilibrium position. The object is then pulled down 0.10 m from the equilibrium position and released. What is the speed of the object when it goes through the equilibrium
A 0.350-kg block moving vertically upward collides with a light vertical spring and compresses it 4.50 cm before coming to rest. If the spring constant is 50.0 N/m, what was the initial speed of the block? (Ignore energy losses to sound and other factors during the collision.)
A 75-kg circus performer jumps from a 5.0-m height onto a trampoline and stretches it downward 0.30 m. Assuming that the trampoline obeys Hooke’s law, (a) How far will it stretch if the performer jumps from a height of 8.0 m? (b) How far will the trampoline stretch if the performer stands still
A vertical spring has a 0.200-kg mass attached to it. The mass is released from rest and falls 22.3 cm before stopping. (a) Determine the spring constant. (b) Determine the speed of the mass when it has fallen only 10.0 cm.
A 0.250-kg ball is dropped from a height of 10.0 cm onto a spring, as illustrated in Fig. 13.24. If the spring has a spring constant of 60.0 N/m,(a) What distance will the spring be compressed? (Neglect energy loss during collision.) (b) On recoiling upward, how high will the ball go?
A 0.50-kg mass oscillates in simple harmonic motion on a spring with a spring constant of 200 N/m. What are (a) The period and (b) The frequency of the oscillation?
The simple pendulum in a tall clock is 0.75 m long. What are (a) The period and (b) The frequency of this pendulum?
How much mass should be at the end of a spring (k = 100 N/m) in order to have a period of 2.0 s?
If the frequency of a mass–spring system is 1.50 Hz and the mass on the spring is 5.00 kg, what is the spring constant?
A breeze sets a suspended lamp into oscillation. If the period is 1.0 s, what is the distance from the ceiling to the lamp at the lowest point? Assume that the lamp is a point mass and acts as a simple pendulum.
Write the general equation of motion for a mass that is on a horizontal frictionless surface and is connected to a spring at equilibrium (a) If the mass is initially pulled in the axis from the spring (stretched) and released, and (b) If the mass is pushed in the axis toward the spring
The equation of motion for an oscillator in vertical SHM is given by y = (0.10 m) sin[(100 rad/s)t] What are the (a) Amplitude, (b) Frequency, and (c) Period of this motion?
The displacement of an object is given by y = (5.0 cm) cos[(20π rad/s)t]. What are the object’s (a) Amplitude, (b) Frequency, and (c) Period of oscillation?
If the displacement of an oscillator in SHM is described by the equation y = (0.25 m) cos [(314rad/s)t], where y is in meters and t is in seconds, what is the position of the oscillator at (a) t = 0, (b) t = 5.0s, and (c) t = 15s?
The equation of motion of a SHM oscillator is x = (0.50m) sin(2πf)t, where x is in meters and t is in seconds. If the position of the oscillator is at x = 0.25 m at t = 0.25s, what is the frequency of the oscillator?
The oscillations of two oscillating mass€“spring systems are graphed in Fig. 13.25. The mass in System A is four times that in System B.(a) Compared with System B, System A has (1) more, (2) the same, or (3) less energy. Why? (b) Calculate the ratio of energy between System B and System
Show that the total energy of a mass–spring system in simple harmonic motion is given by ½ mw2A2.
Show that for a pendulum to oscillate at the same frequency as a mass on a spring, the pendulum’s length must be given by L = mg/k.
The velocity of a vertically oscillating mass–spring system is given by v = (0.65 m/s) sin [(4 rad/s)t]. Determine (a) The amplitude and (b) The maximum acceleration of this oscillator.
(a) If the mass in a mass–spring system is halved, the new period is (1) 2, (2) √2, (3) 1/√2, (4) 1/2 times the old period. Why? (b) If the initial period is 3.0 s and the mass is reduced to 1/3 of its initial value, what is the new period?
(a) If the spring constant in a mass–spring system is halved, the new period is (1) 2, (2) √2, (3) 1/√2, (4) ½ times the old period. Why? (b) If the initial period is 2.0 s and the spring constant is reduced to 1/3 of its initial value, what is the new period?
Students use a simple pendulum with a length of 36.90 cm to measure the acceleration of gravity at the location of their school. If it takes 12.20 s for the pendulum to complete ten oscillations, what is the experimental value of g at the school?
The equation of motion of a particle in vertical SHM is given by y = (10 cm) sin [(0.50 rad/s)t]. What are the particle’s (a) Displacement, (b) Velocity, and (c) Acceleration at t = 1.0s?
What is the maximum elastic potential energy of a simple horizontal mass–spring oscillator whose equation of motion is given by x = (0.350 m) sin[(7 rad/s)t]? The mass on the end of the spring is 0.900 kg.
Two masses oscillate on light springs. The second mass is half of the first and its spring constant is twice that of the first. Which system will have the greater frequency, and what is the ratio of the frequency of the second mass to that of the first mass?
During an earthquake, the floor of an apartment building is measured to oscillate in approximately simple harmonic motion with a period of 1.95 seconds and an amplitude of 8.65 cm. Determine the maximum speed and acceleration of the floor during this motion.
(a) If a pendulum clock were taken to the Moon, where the acceleration due to gravity is only one-sixth (assume the figure to be exact) that on the Earth, will the period of vibration (1) increase, (2) remain the same, or (3) decrease? Why? (b) If the period on the Earth is 2.0 s, what is the
The motion of a particle is described by the curve for System A in Fig. 13.25.(a) Write the equation of motion in terms of a sine or cosine function. (b) If the spring constant is 20 N/m, what is the mass of the object?
The motion of a 0.25-kg mass oscillating on a light spring is described by the curve for System B in Fig. 13.25.(a) Write the equation for the displacement of the mass as a function of time. (b) What is the spring constant of the spring?
The forces acting on a simple pendulum are shown in Fig. 13.26.(a) Show that, for the small angle approximation (sin Î¸ ‰ˆ Î¸), the force producing the motion has the same form as Hooke€™s law. (b) Show by analogy with a mass on a spring that the period
The acceleration as a function of time of a mass–spring system is given by a = (0.60 m/s2) sin[(2 rad/s)t]. If the spring constant is 10 N/m, what are (a) The amplitude, (b) The initial velocity and (c) The mass of the object?
A clock uses a pendulum that is 75 cm long. The clock is accidentally broken, and when it is repaired, the length of the pendulum is shortened by 2.0 mm. Consider the pendulum to be a simple pendulum. (a) Will the repaired clock gain or lose time? (b) By how much will the time indicated by the
The velocity of a vertically oscillating 5.00-kg mass on a spring is given by v = (-0.600 m/s). (a) Determine the equation of motion (y). (b) Where does the motion start and in what direction does the object move initially and with what speed? (c) Determine the period of the motion. (d)
A wave on a rope that measures 10 m long takes 2.0 s to travel the whole rope. If the wavelength of the wave is 2.5 m, what is the frequency of oscillation of any piece of the rope?
The frequency of a simple harmonic oscillator is doubled from 0.25 Hz to 0.50 Hz. What is the change in its period?
Dolphins and bats determine the location of their prey using echolocation (see Conceptual Question 15). If it takes for a bat to receive the ultrasonic sound wave reflected off a mosquito, how far is the mosquito from the bat? Take the speed of sound as 345 m/s.
Light waves travel in a vacuum at a speed of 3.00 x 108 m/s. The frequency of blue light is about 6 x 108 m/s. What is the approximate wavelength of the light?
A sonar generator on a submarine produces periodic ultrasonic waves at a frequency of 2.50 MHz. The wave-length of the waves in seawater is 4.80 x 10-4 m. When the generator is directed downward, an echo reflected from the ocean floor is received 10.0 s later. How deep is the ocean at that point?
The range of sound frequencies audible to the human ear extends from about 20 Hz to 20 kHz. If the speed of sound in air is 345 m/s, what are the wavelength limits of this audible range?
The AM frequencies on a radio dial range from 550 kHz to 1600 kHz, and the FM frequencies range from 88.0 MHz to 108 MHz. All of these radio waves travel at a speed of 3.00 x 108 m/s (speed of light). (a) Compared with the FM frequencies, the AM frequencies have (1) longer, (2) the same, or (3)
Fig. 13.27a shows a snapshot of a wave traveling on a rope, and Fig. 13.27b describes the position as a function of time of a point on the rope.(a) What is the amplitude of the traveling wave? (b) What is the wavelength of the wave? (c) What is the period of the wave? (d) What is the wave speed?
Assume that P and S (primary and secondary) waves from an earthquake with a focus near the Earth’s surface travel through the Earth at nearly constant but different average speeds. A monitoring station that is 1000 km from the epicenter detected the S wave to arrive at 42 s after the arrival of
The speed of longitudinal waves traveling in a long, solid rod is given by v = √Y/p, where Y is Young’s modulus and is the density of the solid. If a disturbance has a frequency of 40 Hz, what is the wavelength of the waves it produces in (a) An aluminum rod and (b) A copper rod?
Fred strikes a steel train rail with a hammer at a frequency of 2.50 Hz, and Wilma puts her ear to the rail 1.0 km away. (a) How long after the first strike does Wilma hear the sound? (b) What is the time interval between the successive sound pulses she hears?
An object of mass 0.50 kg is attached to a spring with spring constant 10 N/m. If the object is pulled down 0.050 m from the equilibrium position and released, what is its maximum speed?
Refer to the wave shown in Fig. 13.27 (Exercise 56).(a) Locate the points on the rope that have a maximum speed. Determine (b) The maximum speed, and (c) The distance between successive high and low spots on the string.
If the frequency of the third harmonic of a vibrating string is 600 Hz, what is the frequency of the first harmonic?
The fundamental frequency of a stretched string is 150 Hz. What are the frequencies of (a) The second harmonic and (b) The third harmonic?
If the frequency of the fifth harmonic of a vibrating string is 425 Hz, what is the frequency of the second harmonic?
A standing wave is formed in a stretched string that is 3.0 m long. What are the wavelengths of (a) The first harmonic and (b) The second harmonic?
If the wavelength of the third harmonic on a string is 5.0 m, what is the length of the string?

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