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physics
oscillations mechanical waves

Questions and Answers of Oscillations Mechanical Waves

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
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
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
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
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,
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)
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
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
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
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)
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
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
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)
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)
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
(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
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
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
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
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 =
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
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
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
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
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
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
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
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
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
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,
(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
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 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
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
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
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
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
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
(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
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
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
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
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
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
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
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
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,
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
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)
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
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
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
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,
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
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
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,
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
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
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.
(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
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
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
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
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
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
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
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
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
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
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
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
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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