Responsible and read street signs
I'll just find out the path difference between the waves at the starting point. At infinity, the path difference will be zero because the observer will be infinitely far away from both. As the observer goes farther, the path difference keeps reducing till it reaches zero as the observer reaches infinity.
<span>Path difference at starting point = Distance from lower speaker - Distance from upper speaker = √((3)² + (2.5)²) - 2.5 = 1.405 m </span>
<span>Now to find wavelength. </span>
<span>Speed of sound in air at 20 degrees C = 343 m/s </span>
<span>Wavelength = 343 / 686 = 0.5 m </span>
<span>Destructive interference occurs when path difference = (2n + 1)λ/2 where n is an integer. </span>
<span>Maximum n possible can be found by, </span>
<span>(2n + 1)λ/2 < 1.405 </span>
<span>(2n + 1) < (1.4)(2) / (0.5) </span>
<span>2n < 5.6 - 1 </span>
<span>2n < 4.6 </span>
<span>n < 2.3 </span>
<span>So, we have 3 values of n, 0, 1 and 2. </span>
<span>Path differences are, λ/2, 3λ/2 and 5λ/2 which have values 0.25 m , 0.75 m and 1.25 m </span>
<span>But the question asks for distance from starting point. (sheesh!!) </span>
<span>Lets say the observer walked x distance. </span>
<span>Path difference = √((3)² + (2.5 + x)²) - (2.5 + x) </span>
<span>Equate this expression to the values obtained above to get the different values of x. </span>
Answer:
Nicholas' speed: 61.9772 miles/hour
current's speed: 6.8864 miles/hour
Explanation:
Let's call Nicholas's speed "x", and the current speed "y".
Going downstream, the total speed is x+y, and we can formulate the equation:
(x+y)*44 = 3030 -> x+y = 68.8636 miles/hour
Going upstream, the total speed is x-y, and we can formulate the equation:
(x-y)*55 = 3030 -> x-y = 55.0909 miles/hour
If we sum both equations, we have that:
2x = 123.9545
x = 61.9772 miles/hour
Now, to know the current speed, we just apply "x" value in one of the equations:
x+y = 68.8636 -> 61.9772 + y = 68.8636 -> y = 6.8864 miles/hour
Answer:
See the answers below
Explanation:
This problem and its respective questions can be easily solved using Newton's law of universal gravitation. Which can be calculated by means of the following expression.
where:
G = it is the universal gravitation constant. = 6.673 x 10⁻¹¹ [N*m²/kg²]
m1 = mass of the first body [kg]
m2 = mass of the second body [kg]
r = distance among the bodies [m]
a. the mass of one is doubled?
When this happens we see that the force is increased twice as well, since the mass is in the numerator of the expression.
b. The masses of both are doubled?
If both masses are doubled the force is increased to four times its original value since the terms of the masses are in the numerator of the expression.
c. The distance between them is doubled?
In this case the force is decreased to half of its original value, since the distance is in the denominator of the expression of universal gravitation.
Answer:
96%
Explanation
Let A the total area of the galaxy, is modeled as a disc:
A = πR^2 = π (25 kpc)^2
And let a be the area that astronomers are able to see:
a = πr^2 = π(5 kpc)^2
The percentage that can be seen is equal to 100 times the ratio of the areas, of the galaxy and the "visible" part:
P = 100 a/A = (5/25)^2 = 100/25 = 4%
Therefore, the percentage of the galaxy not included, i.e. not seen is:
(100-4)% = 96%
