a. yes
b. no
Because the path difference is equal to the wavelength of the sound, the sound originating at the two speakers will interfere constructively at your location and you will perceive a louder sound.
Part B. What is the shortest distance d you need to walk forward to be at a point where you cannot hear the speakers? The forward direction is defined as being perpendicular to a line joining the two speakers and you start walking from the line that joins the two speakers.
Express your answers in meters to three significant figures.
d = m
The sound will be louder when both loudspeakers are used compared to just one due to constructive interference. The shortest distance you need to walk forward to not hear the sound anymore is 0.250 m, calculated using the condition for destructive interference.
Yes, the sound you hear will be louder than if only one speaker were in use. Given that both the loudspeakers are emitting waves in phase and the path difference is equal to the wavelength, the waves will interfere constructively at your location, which will result in a louder sound. This is because when waves meet while they're in phase, they add together to produce a greater amplitude.
The shortest distance d you would need to walk forward to a point where you can't hear the speakers can be calculated using the path difference. From the condition for destructive interference, we know that the path difference should be an odd multiple of half the wavelength (λ/2). Hence the distance would be [(1/2)*λ] which equals [(1/2)*(speed of sound/frequency)]. So, d = [(1/2)*(344/688)] = 0.250 m after joining the values.
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Yes, the sound will be louder due to constructive interference. The shortest distance the student needs to walk forward to not hear the speakers is 0.25 m.
In this scenario, the student is standing equidistant from two loudspeakers that are emitting sound waves in phase at a frequency of 688 Hz. The speed of sound in air is 344 m/s. Part A of the question asks whether the sound that the student hears will be louder than if only one speaker was in use. The answer is yes. This is because the path difference between the two speakers is equal to the wavelength of the sound, resulting in constructive interference at the student's location.
Part B of the question asks for the shortest distance the student needs to walk forward to be at a point where they cannot hear the speakers. To determine this distance, we need to find the point where the path difference between the two speakers is equal to half a wavelength, resulting in destructive interference. The shortest distance the student needs to walk forward is equal to half the wavelength of the sound. Using the formula wavelength = speed of sound / frequency, we can find the wavelength and calculate the distance.
d = (344 m/s / 688 Hz) / 2 = 0.25 m
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Note: The diagram referred to in the question is attached here as a file.
Answer:
The magnitude of the magnetic field is
Explanation:
The magnetic field can be determined by the relationship:
...............(1)
Were I is the current flowing through the wires
The distance R from point 1 to m is calculated using the pythagora's theorem
Substituting R into equation (1)
Use the formula for the magnetic field created by a long, straight, current-carrying wire (B = μ0I/2π(2d)) to find the magnitude of the magnetic field at point M created by wire 1
To find the magnitude of the magnetic field B1m created at point M by wire 1, we can use the Biot-Savart law. The formula for the magnetic field produced by a straight wire at a distance r from the wire is given by:
B = (μ₀ * I) / (2π * r)
Where:
- B is the magnetic field.
- μ₀ is the permeability of free space, which is a constant approximately equal to 4π x T·m/A.
- I is the current flowing through the wire.
- r is the distance from the wire to the point where you want to calculate the magnetic field.
In your case, the distance from wire 1 to point M is 2d. Therefore, we can calculate the magnetic field B1m due to wire 1 at point M as follows:
B1m = (μ₀ * I1) / (2π * (2d))
Now, we need to consider the direction of the magnetic field. Since point M is located equidistant between two wires, and wire 1 is closer to point M, the magnetic field created by wire 1 at point M will point towards or away from the wire, depending on the direction of the current in wire 1.
If the current in wire 1 is in the same direction as the vector from wire 1 to point M, the magnetic field will point away from wire 1. If the current in wire 1 is in the opposite direction, the magnetic field will point towards wire 1.
In both cases, the magnitude of the magnetic field B1m due to wire 1 at point M is given by the formula mentioned earlier:
B1m = (μ₀ * I1) / (2π * (2d))
This formula gives you the magnitude of the magnetic field at point M due to wire 1. The direction of the field depends on the direction of the current in wire 1 relative to the vector from wire 1 to point M.
Learn more about Magnetic Field here:
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Answer:
The centripetal acceleration of Deimos is .
Explanation:
The centripetal acceleration is defined as:
(1)
Where v is the velocity of Deimos and r is the orbital distance.
Notice that is necessary to determine the velocity first.
The speed of the Deimos can be found by means of the Universal law of gravity:
(2)
Then, replacing Newton's second law in equation 2 it is gotten:
(3)
However, a is the centripetal acceleration since Deimos almost describes a circular motion around Mars:
(4)
Replacing equation 4 in equation 3 it is gotten:
(5)
Where v is the orbital speed, G is the gravitational constant, M is the mass of Mars, and r is the orbital radius.
Finally, equation 4 can be used:
Hence, the centripetal acceleration of Deimos is .
The centripetal acceleration of Deimos, one of Mars' moon, can be calculated using its orbital period and distance from Mars. Convert the time units to seconds and use the formulas for velocity and centripetal acceleration to get an answer of approximately 7.84x10^-5 m/s^2.
To find the centripetal acceleration of Deimos, we can use the formula for centripetal acceleration, which is a =v^2/r , where v is the velocity and r is the radius (distance from Mars to Deimos). The velocity can be found using the formula v = 2πr/T, where T is the period (time for one complete orbit).
First, convert the days into seconds because the SI unit of time in physics is second. So, 1.26 days = 1.26 * 24 * 60 * 60 = 108864 seconds.
Then, calculate the velocity: v = 2 * π * 2.35x10^7m / 108864s = 1.36 km/s.
Finally, substitute v and r into the centripetal acceleration formula: a = (1.36x10^3m/s)^2 / 2.35x10^7m = 7.84x10^-5 m/s^2.
The centripetal acceleration of Deimos is approximately 7.84x10^-5 m/s^2.
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