To practice Problem-Solving Strategy 17.1 for wave interference problems. Two loudspeakers are placed side by side a distance d
= 4.00 m apart. A listener observes maximum constructive interference while standing in front of the loudspeakers, equidistant from both of them. The distance from the listener to the point halfway between the speakers is l = 5.00 m . One of the loudspeakers is then moved directly away from the other. Once the speaker is moved a distance r = 60.0 cm from its original position, the listener, who is not moving, observes destructive interference for the first time. Find the speed of sound v in the air if both speakers emit a tone of frequency 700 Hz .
1 answer:
Complete Question
The compete question is shown on the first uploaded question
Answer:
The speed is
Explanation:
From the question we are told that
The distance of separation is d = 4.00 m
The distance of the listener to the center between the speakers is I = 5.00 m
The change in the distance of the speaker is by
The frequency of both speakers is
Generally the distance of the listener to the first speaker is mathematically represented as
Generally the distance of the listener to second speaker at its new position is
Generally the path difference between the speakers is mathematically represented as
Here is the wavelength which is mathematically represented as
=>
=>
=>
Here n is the order of the maxima with value of n = 1 this because we are considering two adjacent waves
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To solve this problem it is necessary to apply the concepts given in the kinematic equations of movement description.
From the perspective of angular movement, we find the relationship with the tangential movement of velocity through
Where,
Angular velocity
v = Lineal Velocity
R = Radius
At the same time we know that the acceleration is given as the change of speed in a fraction of the time, that is
Where
Angular acceleration
Angular velocity
t = Time
Our values are
Replacing at the previous equation we have that the angular velocity is
Therefore the angular speed of a point on the outer edge of the tires is 66.67rad/s
At the same time the angular acceleration would be
Therefore the angular acceleration of a point on the outer edge of the tires is
3) The work done is D. zero
4) The kinetic energy is B. 180 J
5) The potential energy is A. 120 J
6) The work done depends on B. position
7) The example of non-renewable energy is C. coal
8) The power expended is
9) The efficiency is A. 100%
10) The velocity ratio is 5
Explanation:
3)
The work done by a force acting an object is given by:
where :
F is the magnitude of the force
d is the displacement
is the angle between the direction of the force and the displacement
When the force is applied perpendicular to the direction of motion,
Therefore, the work done is:
4)
The kinetic energy of a body is given by
where
m is the mass of the body
v is its speed
For the girl in this problem, we have
m = 40 kg
v = 3 m/s
Therefore her kinetic energy is
5)
The potential energy of an object is given by
where
m is the mass
is the acceleration of gravity
h is the heigth of the object relative to the ground
For the ball in this problem,
m = 0.4 kg
h = 30 m
So, the potential energy is
6)
A conservative field is a field for which the work done by the field on an object does not depend on the path taken, but only on the initial and final position of the object.
Gravitational and electric fields are examples of conservative fields. In fact:
- When an object is pulled down by gravity (free fall), the work done by the gravitational field only depends on the change in height
between the two points, not on the path taken during the fall
- When an electric charge is pushed by the electric field, the work done by the field depends only on the initial and final position of the charge in the field
For any conservative field, it is possible to define a "potential" function, which represents the energy per unit mass/charge, and depends only on the position of the object.
7.
- Non-renewable energy sources are sources of energy whose rate of consumption is faster than the rate at which they are re-created. Examples of non-renewable sources are coal, oil, natural gas. These energy sources are consumed at a fast rate, while they take million of years to regenerate, so at the current rate they will eventually run out.
- Renewable energy sources are sources of energy that replenish at faster rate than the rate at which it is consumed. Examples of renewable sources are solar energy, wind, hydroelectric power.
Therefore, the example of non-renewable energy in this case is
C. Coal
8.
For an object pushed by a force F and moving at a constant velocity v, the power expended is given by
where F is the force and v is the velocity.
for the rocket in this problem, we have:
F = 10 N is the force propelling the rocket
v = 3000 m/s is its velocity
Substituting into the equation, we find the power expended:
9.
The efficiency of a machine is given by
where
is the energy in input to the machine
is the useful work in output from the machine
For a real machine, the useful work in output is always lower than the energy input, because part of the energy is "wasted" and converted into thermal energy due to the presence of internal frictions. However, for an ideal machine, all the input energy is converted into useful work, so
And therefore the efficiency is
which means 100%.
10.
The velocity ratio of a block and tackle system is the ratio between the distance moved by the effort and the distance moved by the load.
In a block and tackle system, the velocity ratio is also equal to the number of pulleys in the system.
For the system in the problem, there are 5 pulleys: therefore, this means that when the effort moves 5 metres, the load moves 1 metres, therefore the velocity ratio is
Learn more about kinetic and potential energy:
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