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Two small stereo speakers are driven in step by the same variable-frequency oscillator. Their sound is picked up by a microphone arranged as shown in the figure. Assume that the speed of sound is 344 m/s.

 

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A) For what frequencies does their sound at the speakers produce constructive interference?

Express your answer in terms of n (an integer factor).

B) For what frequencies does their sound at the speakers produce destructive interference?
Express your answer in terms of n (an integer factor).

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Tauseef Shaikh
Tauseef ShaikhLv10
24 Mar 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Two identical loudspeakers 10.0 m apart are driven by the same oscillator with a frequency of f = 21.5 Hz (Fig. P17.6) in an area where the speed of sound is 344 m/s. (a) Show that a receiver at point A records a minimum in sound intensity from the two speakers. (b) If the receiver is moved in the plane of the speakers, show that the path it should take so that the intensity remains at a minimum is along with the hyperbola 9x2 − 16y2 = 144 (shown in red-brown in Fig. P17.6). (c) Can the receiver remain at a minimum and move very far away from the two sources? If so, determine the limiting form of the path it must take. If not, explain how far it can go.

Figure P17.6

Chapter 17, Problem 6P, Two identical loudspeakers 10.0 m apart are driven by the same oscillator with a frequency of f =

 

I have written my answers in for the one i may of understood!Any help would be great even explanation on how to dothe parts....PLEASE HELP THANK YOU!!!!!!!!!

B. One can purchase so-called Ceramic speakers which haveavibrating ceramic instead
of a coil-driven cone to produce sound waves. These arecapableof producing
frequencies well above the range of human hearing and, infactare used for sonar and
ultrasound applications. The disks used have aconductivecoating applied to either side
of the disk and the ceramic material reacts to anappliedvoltage by contracting or
expanding by an amount proportional to the voltage.Thesedevices are capacitive rather
than inductive.
1. Write the expression for the impedance of such a speakerinterms of the resistance
and capacitance.

2. Find an expression for the frequency ω at whichtheresistance equals the reactance of
the ceramic speaker, in terms of R and C.

3. With R = 8Ω and C = .25μF, calculate thefrequency ω, withunits, that will give R =
XC .

4. Using ωo for the frequency you calculated in 3,calculatethe total impedance, Z, for
the following frequencies and plot the results on the logplotprovided.

Table
ω/ ωo 10-4 10-3 10-2 10-1 1 10 102 103 104
Xc
Z

6. Locate your answer for part (2) on the plot. What featureofthe plot corresponds to
that answer? [4 points]
7. Describe how to quickly sketch this log-log plot for anRCcircuit with only one
calculation, based on your answer to (6). [5 points]
Impedance
0
1
2
3
4
5
6
7
2 3 4 5 6 7 8 9 10
log(omega)
log(Z)
8. Using the same resistance of 8Ω, what value fortheinductance in an LR circuit would
give XL = 8Ω at the same ωo value calculated in 3?
9. Using ωo for the frequency you calculated in 3,calculatethe total impedance, Z, of the
LR circuit for the following frequencies and plot theresultson the log plot provided.


Table
ω/ ωo 10-4 10-3 10-2 10-1 1 10 102 103 104
XL
Z


Good Vibes: Introduction to Oscillations

 

The conditions that lead to simple harmonic motion are as follows:

There must be a position of stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F⃗  is given by ⃗, where is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released from x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there. 

(c) move to the left until it reaches x= –A and stop there. 

(d) move to the left until it reaches x=−A and then begin to move to the right.

 

 

 

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchanged 

(b) doubled 

(c) halved

 

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

 

Part D

If the frequency is 40 Hz, what is the period T?

Express your answer in seconds.

 


The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents the x-coordinate of the oscillating object, and the horizontal axis represents time.

 

Part E

Which points on the x-axis are located at a distance A from the equilibrium position?

(a) R only

(b) Q only

(c) both R and Q

 

Part F

Suppose that the period is T. Which of the following points on the t-axis are separated by the time interval T?

(a) K and L

(b) K and M 

(c) K and P

(d) L and N 

(e) M and P 

 

 

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.

Part G

What is the period T?

Express your answer in seconds.

 

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

 

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

 

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

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