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3 years ago

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A sound source is located somewhere along the x-axis. Experiments show that the same wave front simultaneously reaches listeners

at x = -7.0 m and x = +3.0 m.
part a) What is the x-coordinate of the source?
part b) A third listener is positioned along the positive y-axis. What is her y-coordinate if the same wave front reaches her at the same instant it does the first two listeners?

1 answer:

guapka [62]3 years ago

6 0

Answer:

a) x₀ = - 2 m , b) y = 4.47 m

Explanation:

A wave travels in the middle with constant speed, let's use the equation of uniform motion

v = d / t

t = d / v

The distance to the first listeners, see attached

d₁ = x₀-x

t = (x₀ +7) / v

The distance to the second listener

d₂ = x - x₀

t = (+ 3- x₀) / v

As the wave arrives at the same time, we can equal the two equations

(x₀ +7) / v = (3 -x₀) / v

x₀ + 7 = 3 - x₀

2 x₀ = 3 - 7

x₀ = -4/2

x₀ = - 2 m

b) The time it takes for the wave to reach the listeners of the x-axis, where the speed of sound is 340 m / s

t = 5/340

t = 0.0147 s

Let's look for the distance the wave travels for the listener axis and

v = d₃ / t

d₃ = v.t

d₃ = 340 * 0.0147

d₃ = 5 m

For the distance component we use the Pythagorean triangle

d₃² = x₀² + y²

y² = d₃² - x₀²

y = √ (d₃² -4)

y = √ (5² -4)

y = 4.47 m

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Explanation:

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Case II:

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By substituting the values

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B. x - t graph

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A position-time (x-t) graph is a graph of the position of an object against (versus) time.

Generally, the slope of the line of a position-time (x-t) graph is typically used to determine or calculate the velocity of an object.

An instantaneous velocity can be defined as the rate of change in position of an object in motion for a short-specified interval of time. Thus, an instantaneous velocity is a quantity that can be found by measuring the slope of a line that is tangent to a point on the graph.

Hence, the x - t graph also referred to as the position-time graph is used for determining the instantaneous velocity from the slope.

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$S(t) = 4t^{2} + 2t + 10$

Differentiating the equation, we have;

$S(t) = 8t + 2$

Substituting the value of "t" into the equation, we have;

$S(5) = 8(5) + 2$

$S(5) = 40 + 2$

S(5) = 42 m/s.

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$p_{i}=p_{f}$ (1)

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$p_{i}=m_{1}V_{i} + m_{2}U_{i}$

$p_{f}=m_{1}V_{f} + m_{2}U_{f}$

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$V_{i}=10 m/s$ is the velocity of Tubby and Libby with the car before the collision

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$U_{i}=0 m/s$ is the velocity of Flubby with the car before the collision

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$U_{f}$ is the velocity of Flubby with the car after the collision

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Finding $U_{f}$ :

$U_{f}=\frac{m_{1}(V_{i}-V_{f})}{m_{2}}$ (3)

$U_{f}=\frac{300 kg(10 m/s-4.12 m/s)}{125 kg}$ (4)

Finally:

$U_{f}=14.1 m/s$

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3 years ago