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physics
oscillations mechanical waves

Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

Suppose a spherical loudspeaker emits sound isotropically at 10 W into a room with completely absorbent walls, floor, and ceiling (an anechoic chamber).(a) What is the intensity of the sound at distance d = 3.0 m from the center of the source?(b) What is the ratio of the wave amplitude at d = 4.0 m
To search for a fossilized dinosaur embedded in rock, paleontologists can use sound waves to produce a computer image of the dinosaur. The image then guides the paleontologist as they dig the dinosaur out of the rock. (The technique is shown in the opening scenes of the movie Jurassic Park.) The
The period of a pulsating variable star may be estimated by considering the star to be executing radial longitudinal pulsations in the fundamental standing wave mode; that is, the star's radius varies periodically with time, with a displacement anti node at the star's surface.(a) Would you expect
A listener at rest (with respect to the air and the ground) hears a signal of frequency f r from a source moving toward him with a velocity of 15 m/s, due east. If the listener then moves toward the approaching source with a velocity of 25m/s, due west, he hears a frequency f2 that differs from f1
A guitar player tunes the fundamental frequency of a guitar string to 440 Hz.(a) What will be the fundamental frequency if she then increases the tension in the string by 20%?(b) What will it be if, instead, she decreases the length along which the string oscillates by sliding her finger from the
In a certain oscillating LC circuit, the total energy is converted from electrical energy in the capacitor to magnetic energy in the inductor in 1.50μs. What are?(a) The period of oscillation and(b) The frequency of oscillation?(c) How long after the magnetic energy is a maximum will it is a
What is the capacitance of an oscillating LC circuit if the maximum charge on the capacitor is I.60μC and the total energy is 140μJ?
In an oscillating LC circuit, L = 1.10 mH and C = 4.00μF. The maximum charge on the capacitor is 3.00μC. Find the maximum current.
The frequency of oscillation of a certain LC circuit is 200 kHz. At time t = 0, plate A of the capacitor has maximum positive charge. At what earliest time t > 0 will(a) Plate A again has maximum positive charge,(b) The other plate of the capacitor have maximum positive charge, and(c) The
An oscillating LC circuit consists of a75.0 mH inductor and a 3.60 pF capacitor. If the maximum charge on the capacitor is 2.90μC, what are?(a) The total energy in the circuit and(b) The maximum current?
A 0.50 kg body oscillates in SHM on a spring that, when 2.0 mm extended from its equilibrium position has an 8.0 N restoring force. What are?(a) The angular frequency of oscillation,(b) The period of oscillation, and(c) The capacitance of an LC circuit with the same period if L is 5.0 H?
The energy in an oscillating LC circuit containing a 1.25 H inductor is 5.70μJ. The maximum charge on the capacitor is 175μC. For a mechanical system with the same period, find the(a) Mass,(b) Spring constant,(c) Maximum displacement, and(d) Maximum speed
LC oscillators have been used in circuits connected to loudspeakers to create some of the sounds of electronic music. What inductance must be used with a 6.7μF capacitor to produce a frequency of 10 kHz, which is near the middle of the audible range of frequencies?
In an oscillating LC circuit with L = 50 mH and C = 4.0μF, the current is initially a maximum. How long will it take before the capacitor is fully charged for the first time?
A single loop consists of inductors (L1, L2 . . .), capacitors (C1, C2 . . .), and resistors (R1, R2 . . .) connected in series as shown, for example, in Figure a. Show that regardless of the sequence of these circuit elements in the loop, the behavior of this circuit is identical shown in Figure b.
In Figure, R = 14.0??, C = 6.20μE, and L = 54.0mH, and the ideal battery has emf ξ = 34.0 V. The switch is kept in position ??a?? for a long time and then thrown to position b. What are the (a) Frequency and (b) Current amplitude of the resulting oscillations?
To construct an oscillating LC system, you can choose from a 10 mH inductor, a 5.0μF capacitor, and a 2.0μF capacitor. What are the(a) Smallest,(b) Second smallest,(c) Second largest, and(d) Largest oscillation frequency that can be set up by these elements in various combinations?
An oscillating LC circuit consisting of a 1.0μF capacitor and a 3.0mH coil has a maximum voltage of 3.0 V. What are?(a) The maximum charge on the capacitor,(b) The maximum current through the circuit, and?(c) The maximum energy is stored in the magnetic field of the coil?
An inductor is connected across a capacitor whose capacitance can be varied by turning a knob. We wish to make the frequency of oscillation of this LC circuit vary linearly with the angle of rotation of the knob, going from 2 x 105 to 4 x 105 Hz as the knob turns through 180°. If L = 1.0mH, plot
A variable capacitor with a range from 10 to 365 pF is used with a coil to form a variable frequency LC circuit to tune the input to a radio.(a) What is the ratio of maximum frequency to minimum frequency that can be obtained with such a capacitor? If this circuit is to obtain frequencies from
A series circuit containing inductance L1 and capacitance C1 oscillates at angular frequency w, A second series circuit, containing inductance L2 and capacitance C2, oscillates at the same angular frequency. In terms of w, what is the angular frequency of oscillation of a series circuit containing
In an oscillating LC circuit with C = 64.0μF, the current is given by i = (1.60) sin (2500t + 0.680), where r is in seconds, i in amperes, and the phase constant in radians.(a) How soon after t = 0 will the current reach its maximum value? What are?(b) The inductance L and(c) The total energy?
In an oscillating LC circuit, when 75.0% of the total energy is stored in the inductor's magnetic field.(a) What multiple of the maximum charge is on the capacitor and(b) What multiple of the maximum current is in the inductor?
In an oscillating LC circuit, L = 25.0 mH and C = 7.80μF. At time t = 0 the current is 9.20 mA, the charge on the capacitor is 3.80μC, and the capacitor is charging. What are?(a) The total energy in the circuit,(b) The maximum charge on the capacitor, and(c) The maximum current?(d) If the charge
An oscillating LC circuit has current amplitude of 7.50 mA, potential amplitude of 250 mV and a capacitance of 220nF. What are?(a) The period of oscillation,(b) The maximum energy stored in the capacitor,(c) The maximum energy stored in the inductor,(d) The maximum rate at which the current
In an oscillating LC circuit, L = 3.00 mH and C = 2.70μF, at t = 0 the charge on the capacitor is zero and the current is 2.00 A. (a) What is the maximum charge that will appear on the capacitor? (b) At what earliest time t > 0 is the rate at which energy is stored in the capacitor greatest
In an oscillating LC circuit in which C = 4.00μF, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 mA. What are?(a) The inductance L and(b) The frequency of the oscillations?(c) How much time is required
Using the loop rule, derive the differential equation for an LC circuit (Eq.31-11).
In an oscillating series RLC circuit, find the time required for the maximum energy present in the capacitor during an oscillation to fall to half its initial value. Assume q = Q at t = 0.
What resistance R should be connected in series with an inductance L = 220 mH and capacitance C = 12.0μF for the maximum charge on the capacitor to decay to 99.0% of its initial value in 50.0 cycles? (Assume w = w)
A single-loop circuit consists of a 7.20Ω resistor, a 12.0 H inductor, and a 3.20μF capacitor. Initially the capacitor has a charge of 6.20μC and the current is zero. Calculate the charge on the capacitor N complete cycles later for(a) N = 5,(b) N = 10, and(c) N = 100.
In an oscillating series RLC circuit, show that ΔU/U, the fraction of the energy lost per cycle of oscillation, is given to a close approximation by 2πR/w L The quantity w L/R is often called the Q of the circuit (for quality). A high-Q circuit has low resistance and a low fractional
A 50.0Ω resistor is connected as in Figure to an ac generator with ξ m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is?(a) 1.00 kHz and(b) 8.00 kHz
(a) At what frequency would a 6.0 mH inductor and a 10μF capacitor have the same reactance?(b) What would the reactance be?(c) Show that this frequency would be the natural frequency of an oscillating circuit with the same L and C.
A 1.50μF capacitor is connected as in Figure to an ac generator with ξ m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is?(a) 1.00 kHz and(b) 8.00 kHz
A 50.0 mH inductor is connected as in Figure to an ac generator with ξ m = 30.0 V. What is the amplitude of the resulting alternating current if the frequency of the emf is?(a) 1.00 kHz and(b) 8.00 kHz
An ac generator with emf ξ = ξ m sin w d t, where ξ m = 25.0 V and w d = 377 rad/s, is connected to a 4.15μF capacitor.(a) What is the maximum value of the current?(b) When the current is a maximum, what is the emf of the generator?(c) When the emf of the generator is -12.5 V and increasing in
An ac generator has emf ξ = ξ m sin (w d t = π/4), where ξ m = 30.0 V w d = 350 rad/s. The current produced in a connected circuit is i (t) = I sin (w d t = 3π/4), where I = 620 mA. At what time after t = 0 does (a) The generator emf first reach a maximum and (b) The
An ac generator has emf ξ = ξ m sin w d t, with ξ m = 25.0 V and w d = 377 rad/s. It is connected to a 12.7 H inductor.(a) What is the maximum value of the current? (b) When the current is a maximum, what is the emf of the generator?(c) When the emf of the generator is -12.5 V and
Remove the inductor from the circuit in Figure and set R = 200Ω, C = 15.0ΩF, f d = 60.0 Hz, and ξ m = 36.0 V. What are?(a) Z,(b) Ф, and(c) I?(d) Draw a phasor diagram.
The current amplitude I versus driving angular frequency w d for a driven RLC circuit is given in Figure, where the vertical axis scale is set by I s = 4.00 A. The inductance is 200μH, and the emf amplitude is 8.0 V. What are? (a) C and (b) R?
Remove the capacitor from the circuit in Figure and set R = 200Ω, L = 230 mH, f d = 60.0 Hz, and ξ m = 36.0 V. What are? (a) Z, (b) Ф, and (c) I? (d) Draw a phasor diagram.
An alternating source with a variable frequency, an inductor with inductance L, and a resistor with resistance R are connected in series. Figure gives the impedance Z of the circuit versus the driving angular frequency w d, with the horizontal axis scale set by w d s = 1600 rad/s. The figure also
In Figure, set R = 200Ω, C = 70.0μF, L = 230mH, f d = 60.0Hz, and ξ m = 36.0 V. What are?(a) Z,(b) Ф, and(c) I?(d) Draw a phasor diagram.
An alternating source with a variable frequency, a capacitor with capacitance C, and a resistor with resistance R are connected in series. Figure gives the impedance Z of the circuit versus the driving angular frequency w d; the curve reaches an asymptote of 500??, and the horizontal scale is set
An electric motor has an effective resistance of 32.0Ω and an inductive reactance of 45.0Ω when working under load. The rms voltage across the alternating source is 420 V. Calculate the rms current.
An alternating source drives a series RLC circuit with emf amplitude of 6.00 V at a phase angle of +30.0°. When the potential difference across the capacitor reaches its maximum positive value of +5.00 V what is the potential difference across the inductor (sign included)?
A coil of inductance 88 mH and unknown resistance and a 0.94μF capacitor are connected in series with an alternating emf of frequency 930 Hz. If the phase constant between the applied voltage and the current is 75°, what is the resistance of the coil?
An alternating emf source with a variable frequency f d connected in series with a 50.0Ω resistor and a 20.0μF capacitor. The emf amplitude is 12.0 V.(a) Draw a phasor diagram for phasor VR (the potential across the resistor) and phasor VC (the potential across the capacitor).(b) At what driving
An RLC circuit such as that of Figure has R = 5.00Ω, C = 20.0μF, L = 1.00 H, and ξ m = 30.0 V. (a) At what angular frequency w d will the current amplitude have its maximum value, as in the resonance curves of Figure? (b) What is this maximum value? At what (c) Lower angular
Figure shows a driven RLC circuit that contains two identical capacitors and two switches. The emf amplitude is set at 12.0 V, and the driving frequency is set at 60.0 Hz. With both switches open, the current leads the emf by 30.9?. With switch S1 closed and switch S2 still open, the emf leads the
(a) In an RLC circuit, can the amplitude of the voltage across an inductor be greater than the amplitude of the generator emf?(b) Consider an RLC circuit with ξ m = 10 V, R = 10Ω, L = 1.0 H, and C = 1.0μF, Find the amplitude of the voltage across the inductor at resonance.
An alternating emf source with a variable frequency f d is connected in series with an 80.0Ω resistor and a 40.0 mH inductor. The emf amplitude is 6.00 V.(a) Draw a phasor diagram for phasor V R (the potential across the resistor) and phasor V L(the potential across the inductor).(b) At what
The fractional half-width Δ w d of a resonance curve, such as the ones in Figure, is the width of the curve at half the maximum value of I. Show that Δ w d / w = R(3C/L)1/2, where w is the angular frequency at resonance. Note that the ratio Δ w d / w increases with R as Figure show
An ac generator with ξ m = 220V and operating at 400 Hz causes oscillations in a series RLC circuit having R = 220Ω, L = 150mH, and C = 24.0μF. Find (a) The capacitive reactance XC, (b) The impedance Z, and (c) The current amplitude I. A second capacitor of the same capacitance
In Figure, a generator with an adjustable frequency of oscillation is connected to resistance R = 100??, inductances L1 = 1.70 mH and L2 = 2.30 mH, and capacitances C1 = 4.00μF, C2 = 2.50μF, and C3 = 3.50μF. (a) What is the resonant frequency of the circuit? What happens to the resonant
What is the maximum value of an ac voltage whose rms value is 100 V?
What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.60 A?
An ac voltmeter with large impedance is connected in turn across the inductor, the capacitor, and the resistor in a series circuit having an alternating emf of 100 V (rms); the meter gives the same reading in volts in each case. What is this reading?
An air conditioner connected to a 120 V rms ac line is equivalent to a 12.0Ω resistance and a 1.30Ω inductive reactance in series. Calculate (a) The impedance of the air conditioner and (b) The average rate at which energy is supplied to the appliance.
For Figure show that the average rate at which energy is dissipated in resistance R is a maximum when R is equal to the internal resistance r of the ac generator. (In the text discussion we tacitly assumed that r =0.)
(a) What is the power factor?(b) Does the current lead or lag the emf?(c) Is the circuit in the box largely inductive or largely capacitive?(d) Is the circuit in the box in resonance?(e) Must there be a capacitor in the box?(f) An inductor?(g) A resistor?(h) At what average rate is energy delivered
In a series oscillating RLC circuit, R = 16.0Ω, C = 31.2μF, L = 9.20mH, and ξ = ξ m sin w d t with ξ m = 45.0 V and w d =3000 rad/s. For time t = 0.442ms find(a) The rate P g at which energy is being supplied by the generator,(b) The rate P C, at which the energy in the capacitor is
In an RLC circuit such as that of Fig. 3I-7 assume that R = 5.00Ω, L = 60.0 mH, f d = 60.0 Hz, and ξ m = 30.0 V. For what values of the capacitance would the average rate at which energy is dissipated in the resistance be? (a) A maximum and (b) A minimum? What are? (c) The maximum
A typical light dimmer used to dim the stage lights in a theater consists of a variable inductor L (whose inductance is adjustable between zero and L max) connected in series with a lightbulb B, as shown in Figure. The electrical supply is 120 V (rms) at 60.0 Hz; the light bulb is rated at l20 V
In Figure, R = 15.0Ω, C = 4.70μF, and L = 25.0 mH. The generator provides an emf with rms voltage 75.0 V and frequency 550 Hz. (a) What is the rms current? What is the rms voltage across? (b) R, (c) C, (d) L, (e) C and L together, and (f) R, C, and L together? At what average rate
Figure shows an "autotransformer." It consists of a single coil (with an iron core). Three taps Ti are provided. Between taps T1 and T2 there are 200 turns, and between taps T2 and T3 there are 800 turns. Any two taps can be chosen as the primary terminals, and any two taps can be chosen as the
A transformer has 500 primary turns and 10 secondary turns.(a) If V p is 720 V (rms), what is V s with an open circuit? If the secondary now has a resistive load of 15Ω, what is the current in the(b) Primary and(c) Secondary?
A generator supplies 100 V to a transformer's primary coil, which has 50 turns. If the secondary coil has 500 turns, what is the secondary voltage?
An ac generator provides emf to a resistive load in a remote factory over a two-cable transmission line. At the factory a step-down transformer reduces the voltage from its (rms) transmission value V t to a much lower value that is safe and convenient for use in the factory. The transmission line
An electric motor connected to a 120 V 60.0 Hz ac outlet does mechanical work at the rate of 0.100 hp (1 hp = 746 W).(a) If the motor draws an rms current of 0.650A, what is its effective resistance, relative to power transfer?(b) Is this the same as the resistance of the motor's coils, as measured
In Figure, a three-phase generator G produces electrical power that is transmitted by means of three wires. The electric potentials (each relative to a common reference level) are V1 = A sin w d t for wire 1, V 2 = A sin (w d t = 120?) for wire 2, and V 3 = A sin (w d t = 240?) for wire 3. Some
A 1.50μF capacitor has a capacitive reactance of 12.0 Q.(a) What must be its operating frequency?(b) What will be the capacitive reactance if the frequency is doubled?
For a certain driven series RLC circuit, the maximum generator emf is 125V and the maximum current is 3.20 A. If the current leads the generator emf by 0.982 rad, what are the(a) Impedance and(b) Resistance of the circuit?(c) Is the circuit predominantly capacitive or inductive?
An oscillating LC circuit has an inductance of 3.00 mH and a capacitance of 10.0μE Calculate the(a) Angular frequency and(b) Period of the oscillation.(c) At time t = 0, the capacitor is charged to 200μC and the current is zero. Roughly sketch the charge on the capacitor as a function of time.
In a certain series RLC circuit being driven at a frequency of 60.0 Hz, the maximum voltage across the inductor is 2.00 times the maximum voltage across the resistor and 2.00 times the maximum voltage across the capacitor.(a) By what angle does the current lag the generator emf?(b) If the maximum
What capacitance would you connect across a 1.30 mH inductor to make the resulting oscillator resonate at 3.50 kHz?
An LC circuit oscillates at a frequency of 10.4 kHz.(a) If the capacitance is 340μE, what is the inductance?(b) If the maximum current is 7.20 mA, what is the total energy in the circuit?(c) What is the maximum charge on the capacitor?
A series RLC circuit has a resonant frequency of 6.00 kHz. When it is driven at 8.00 kHz, it has an impedance of 1.00kΩ and a phase constant of 45°.What are(a) R,(b) L, and(c) C for this circuit?
A capacitor of capacitance 158μF and an inductor form an LC circuit that oscillates at 8.15 kHz, with current amplitude of 4.21 mA. What are?(a) The inductance,(b) The total energy in the circuit, and(c) The maximum charge on the capacitor?
A series RLC circuit is driven in such a way that the maximum voltage across the inductor is 1.50 times the maximum voltage across the capacitor and 2.00 times the maximum voltage across the resistor.(a) What is ф for the circuit?(b) Is the circuit inductive, capacitive, or in resonance? The
An RLC circuit is driven by a generator with an emf amplitude of 80.0 V and a current amplitude of 1.25 A. The current leads the emf by 0.650 rad. What are the(a) Impedance and(b) Resistance of the circuit?(c) Is the circuit inductive, capacitive, or in resonance?
A 45.0 mH inductor has a reactance of 1.30kΩ.(a) What is its operating frequency?(b) What is the capacitance of a capacitor with the same reactance at that frequency? If the frequency is doubled, what is the new reactance of?(c) The inductor and(d) The capacitor?
A generator of frequency 3000 Hz drives a series RLC circuit with emf amplitude of 120 V. The resistance is 40.0Ω, the capacitance is 1.60μF, and the inductance is 850μH. What are?(a) The phase constant in radians and(b) The current amplitude?(c) Is the circuit capacitive, inductive, or in
A 1.50 mH inductor in an oscillating LC circuit stores a maximum energy of 10.0μJ. What is the maximum current?
A generator with an adjustable frequency of oscillation is wired in series to an inductor of L = 2.50 mH and a capacitor of C = 3.00μF. At what frequency does the generator produce the largest possible current amplitude in the circuit?
A series RLC circuit is driven by an alternating source at a frequency of 400 Hz and emf amplitude of 90.0 V. The resistance is 20.0Ω, the capacitance is 12.1μF, and the inductance is 24.2 mH. What is the rms potential difference across?(a) The resistor,(b) The capacitor, and(c) The inductor?(d)
(a) In an oscillating LC circuit, in terms of the maximum charge Q on the capacitor, what is the charge there when the energy in the electric field is 50.0% of that in the magnetic field?(b) What fraction of a period must elapse following the time the capacitor is fully charged for this condition
When under load and operating at an rms voltage of 220 V a certain electric motor draws an rms current of 3.00 A. It has a resistance of 24.0Ω and no capacitive reactance. What is its inductive reactance?
For a sinusoid ally driven series RLC circuit, show that over one complete cycle with period T(a) The energy stored in the capacitor does not change; (b) The energy stored in the inductor does not change;(c) The driving emf device supplies energy (1/2T) ξ m I cos ф; and(d) The resistor
When the generator emf in Sample Problem 31-7 is a maximum, what is the voltage across?(a) The generator,(b) The resistance,(c) The capacitance, and(d) The inductance?(e) By summing these with appropriate signs, verify that the loop rule is satisfied.
An ac generator produces emf ξ = ξ sin (w d t – π/4), where ξ m = 30.0 V and w d = 350 rad/s.The current in the circuit attached to the generator is i(r) = I sin (w d t + π/4), where I = 620 mA.(a) At what time after t = 0 does the generator emf first reach a maximum?(b) At what time after t
However, a transformer can be used to "transform" resistances, making them behave electrically as if they were larger or smaller than they actually are.(a) Sketch the primary and secondary coils of a transformer that can be introduced between the amplifier and the speaker in Figure to match the
A series circuit with resistor-inductor-capacitor combination R1, L1, C1, has the same resonant frequency as a second circuit with a different combination R2, L2, C2. You now connect the two combinations in series. Show that this new circuit has the same resonant frequency as the separate circuits.
With switch S1 closed and the other two switches open, the circuit has a time constant τ C. With switch S2 closed and the other two switches open, the circuit has a time constant τ L with switch S3 closed and the other two switches open, the circuit oscillates with a period T. Show that T =
The ac generator in Figure supplies 120V at 60.0 Hz. With the switch open as in the diagram, the current leads the generator emf by 20.0?. With the switch in position 1, the current lags the generator emf by 10.0?. When the switch is in position 2, the current amplitude is 2.00 A. What are? (a)
In an oscillating LC circuit, L = 8.00 mH and C = 1.40μF. At time t = 0, the current is maximum at 12.0 mA.(a) What is the maximum charge on the capacitor during the oscillations?(b) At what earliest time t > 0 is the rate of change of energy in the capacitor maximum?(c) What is that maximum
A series RLC circuit is driven by a generator at frequency 1050 Hz. The inductance is 90.0 mH; the capacitance is 0.500 pF; and the phase constant has a magnitude of 60.0° (you should supply the appropriate sign for the angle).(a) What is the resistance? To increase the current amplitude in the
A series RLC circuit is driven by a generator at a frequency of 2000 Hz and emf amplitude of 170 V. The inductance is 60.0 mH, the capacitance is 0.400μF, and the resistance is 200Ω. (a) What is the phase constant in radians?(b) What is the current amplitude?
A 7.00μF capacitor has an initial potential of 12.0 V when it is connected across an inductor. The combination then oscillates at a frequency of 715 Hz. What is the inductance of the inductor?

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