Answer:
3688 km/h
Explanation:
Given:-
- The speed of vehicle relative to earth, vs_e = 3760 km/h
- The relative speed of command and motor, v_c/m = 90 km/h
- The mass of command = m
- The mass of motor = 4m
Find:-
What is the speed of the command module relative to Earth just after the separation?
Solution:-
- Consider the space vehicle as a system that detaches itself into two parts ( command and motor ). We will assume that the gravitational pull due to Earth on the space vehicle is negligible. With that assumption we have our system in isolation. We will apply the principle of conservation of linear momentum on the system as follows:
Initial momentum = Final momentum
Pi = Pf
M*vs_e = m*vc_e + 4m*vm_e
Where,
M = m + 4m = 5m
vc_e = Velocity of command relative to earth
vm_e = Velocity of motor relative to earth
- We will develop a relation of velocities of command and motor in the frame of earth as follows:
vm_e = v_c/m + vc_e
- Substituting (vm_e) from Equation 2 into Equation 1, we have:
5m*vs_e = m*vc_e + 4m*(v_c/m + vc_e)
5m*vs_e = 5m*vc_e + 4m*(v_c/m)
- Solve for vc_e:
5m*vs_e - 4m*(v_c/m) = 5m*vc_e
vs_e - 0.8*(v_c/m) = vc_e
- Plug in values and evaluate vc_e:
vc_e = 3760 - 0.8*(90)
vc_e = 3,688 km/h
Answer:
The command module is traveling at 3832 km/h after the separation.
Explanation:
Let's call the mass of the module M, and the mass of the motor is 4M. The total mass of the vehicle, then, is M + 4M = 5M.
Now, momentum = force x distance.
Thus, momentum of the vehicle before separation 3760 x 5M = 18800M kg-km/h.
Let's call the velocity of the motor v. So the velocity of the module must be v + 93.
Now, after the separation, the momentum of the motor will be 4Mv, and the momentum of the module is M(v + 90) = Mv + 90M. The total momentum is 4MV + Mv + 90M = 5Mv + 90M.
From conservation of momentum that says initial momentum equals final momentum, we have;
18800M = 5Mv + 90M
Divide both sides by M to get;
18800 = 5v + 90
18800 - 90 = 5v
18710 = 5v
v = 18710/5
v = 3742 km/h
But v is the velocity of the motor, so we have to add 90 to get the velocity of the module, thus, velocity of module = 3742 + 90 = 3832
So the command module is traveling at 3832 km/h after the separation.
After a fall, a 75 kg rock climber finds himself dangling from the end of a rope that had been 18 m long and 11 mm in diameter but has stretched by 2.1 cm. For the rope, calculate (a) the strain, (b) the stress, and (c) the Young's modulus.
Answer:
(A) Strain = 0.0012
(b) Stress [tex]=77.44\times 10^5N/m^2[/tex]
(c) Young's modulus [tex]=6.45\times 10^9N/m^2[/tex]
Explanation:
Mass of the rock m = 75 kg
So weight of the rock [tex]F=mg=75\times 9.8=735N[/tex]
Length of the rope l = 18 m
Diameter of the rope d = 11 mm
Change in length of rope [tex]\Delta l=2.1cm =0.021m[/tex]
So radius r = 5.5 mm = 0.0055 m
Cross sectional area [tex]A=\pi r^2[/tex]
[tex]A=3.14\times 0.0055^2=9.49\times 10^{-5}m^2[/tex]
(a) Strain is equal to ratio change in length to original length
So strain [tex]=\frac{\Delta l}{l}=\frac{0.021}{18}=0.0012[/tex]
(b) Stress [tex]=\frac{Weight}{area}[/tex]
[tex]=\frac{735}{9.49\times 10^{-5}}=77.44\times 10^5N/m^2[/tex]
(c) Young's modulus is equal to ratio of stress and strain
So young's modulus [tex]=\frac{77.44\times 10^5}{0.0012}=6.45\times 10^9N/m^2[/tex]
The electrical resistance of a metallic conductor is inversely proportional to its
Answer:
Cross sectional area
Explanation:
Resistance of a metallic conductor is the measure of its opposition to the flow of electric current. Resistance is known to be directly proportional to the temperature which means as the temperature is increased, its resistance increases too and vice versa.
The resistance however has an inverse relationship with the cross sectional area of the metallic conductor. This means as the resistance increases the cross sectional area decreases and vice versa.
In a parallel circuit, each resistor has:
A: no connection to the voltage source
B: a shared connection to the voltage source
C: its own connection to the voltage source
Answer:
C
Explanation:
Answer:
In a parallel circuit, each resistor has: its own connection to the voltage source.
Explanation:
Twin space probes have a mass of 722 kg each. If the gravitational force between the two space probes is 8.61
10-16 N. what is the distance between them?
7.48 x 103 meters
Answer:200×10^5 meters
Explanation:
Answer:
200×10^5 meters
Explanation:
EDGE
The range of wavelengths for visible light is from 3.9*10^-7m. What is the corresponding range of frequencies for visible light
Answer:
from 7.69×10¹⁵ Hz
Explanation:
Frequency: This can be defined as the number of complete cycle a wave complete in one seconds, the S.I unit of frequency is Hertz (Hz).
From the question,
v = λf............. Equation 1
Where v = speed of visible light in air, λ = wave length of visible light, f = frequency of visible light.
make f the subject of the equation
f = v/λ.................... Equation 2
Note: all electromagnetic wave have the same speed = 3×10⁸ m/s
Given: v = 3×10⁸ m/s, λ = from 3.9×10⁻⁷ m
Substitute into equation 2
f = 3×10⁸/ 3.9×10⁻⁷
f = 7.69×10¹⁵ Hz
Hence the range of the frequencies for visible light = from 7.69×10¹⁵ Hz
Final answer:
The range of frequencies for visible light, corresponding to wavelengths from about 400 nm to 700 nm, extends from approximately 4.28 × 10¹⁴ Hz to 7.50 × 10¹⁴ Hz.
Explanation:
The range of wavelengths for visible light is commonly accepted to be from about 400 nm to 700 nm. To find the corresponding range of frequencies for visible light, we use the formula c = λf, where c is the speed of light (≈ 3.00 × 10¸ m/s), λ is the wavelength in meters, and f is the frequency in hertz (Hz). For the visible light range, converting nanometers to meters (× 10⁻⁹), we calculate the frequencies at both ends of the spectrum: for 400 nm (4.00 × 10⁻⁷ m), the frequency is approximately 7.50 × 10¹⁴ Hz, and for 700 nm (7.00 × 10⁻⁷ m), it's approximately 4.28 × 10¹⁴ Hz. Therefore, the range of frequencies for visible light extends approximately from 4.28 × 10¹⁴ Hz to 7.50 × 10¹⁴ Hz.
A 12 volt car battery is connected to a 3 ohm brake light. What is the current carrying energy to the lights?
Answer:
4 A
Explanation:
V = IR, where V=voltage, I=current, R=resistance. This is Ohm's Law. (remember that for units V = volts, Ω = ohms, A = amperes.)
V = IR
12 V = I * 3 Ω
12/3 = I
I = 4 A
The current flowing through the 3-ohm brake light connected to a 12-volt car battery is 4 amperes (A).
To find the current carrying energy to the 3-ohm brake light on a 12-volt car battery, we use Ohm's Law, which states that current (I) is equal to the voltage (V) divided by resistance (R). In this case, the voltage is 12 volts, and the resistance is 3 ohms.
Applying Ohm's Law: I = V / R
I = 12V / 3Ω
I = 4A.
Therefore, the current through the brake light is 4 amperes (A).
two objects with the same mass move with the same speed but in opposite directions. A. Kinetic energies are equal B. Kinetic energies are opposite in magnitude C. Kinetic energies of the higher objects is greater D. Kinetic energy of the lower object is greater
this is the best answer for you
When two objects collide there will be a force acting on them both and their individual kinetic energies and momenta may alter. As you know already, energy is always conserved but in a collision some, or all of the kinetic energy may be ... of the same mass and traveling at the same speed but in opposite directions collided ...
Answer:
A
Explanation:
Using the formula 1/2mV² both kinetic energy are equal irrespective of the direction.
A horizontal force of at least 150N is required to start moving a 750N crate initialy at rest on a horizontal fioor the coefficient of static friction between the crate and the floor is?
Answer:A 25 kg block is initially at rest on a rough, horizontal surface. A horizontal ... The coefficient of static friction between a 10 kg object and the floor is 0.50.
Explanation:
Sound moves at a speed of 343 meters per second through air, a gas.
Which pairing is most accurate for how sound will travel through
liquid and solid?
Answer:
need more info
Explanation:
You can determine the index of refraction of a substance by measuring its critical angle for total internal reflection. True or False
Answer:
True. Hope you have a good day, internet stranger. :)
Brainly i can you please help me
Answer:
bet
Explanation:
A 0.200 kg air-track glider moving at 1.20 m/s bumps into a 0.600 kg glider at rest.
a.) Find the total kinetic energy after collision if the collision is elastic.
b.) Find the total kinetic energy after collision if the collision is completely inelastic.
Answer:
a) 0.144J
b) 0.12J
Explanation:
A 0.200 kg air-track glider moving at 1.20 m/s bumps into a 0.600 kg glider at rest. a.) Find the total kinetic energy after collision if the collision is elastic. b.) Find the total kinetic energy after collision if the collision is completely inelastic.
Given that
M1 = 0.2kg
M2 = 0.6kg
U1 = 1.2 m/s
Since both momentum and energy are conserved in elastic collisions, the total kinetic energy after collision will be
1/2M1U^2 + 1/2M2U^2
1/2 × 0.2 × 1.2^2 + 0
K.E = 0.144J
B) In elastic collision, only momentum is conserved
M1U1 + M2U2 = (M1 + M2)V
U2 = 0 since the object is at rest
0.2×1.2 + 0 = (0.2 + 0.6)V
0.24 = 0.8V
V = 0.24/0.8
V = 0.3 m/s
K.E = 1/2(M1+M2)V
K.E = 1/2 (0.2 + 0.6) × 0.3
K.E = 0.4 × 0.3
K.E = 0.12J
Answer:
The other person is almost right, but I see where the numbers got fudged
Explanation:
Answer:a) 0.144Jb) 0.036J
Explanation: A 0.200 kg air-track glider moving at 1.20 m/s bumps into a 0.600 kg glider at rest. a.) Find the total kinetic energy after collision if the collision is elastic. b.) Find the total kinetic energy after collision if the collision is completely inelastic. Given that M1 = 0.2kgM2 = 0.6kgU1 = 1.2 m/s Since both momentum and energy are conserved in elastic collisions, the total kinetic energy after collision will be1/2M1U^2 + 1/2M2U^21/2 × 0.2 × 1.2^2 + 0K.E = 0.144J
B) This is where the other person's wrong:
m1u1+m2u2=(m1+m2)V
V=(0.200kg*1.20m/s)/(0.200kg+0.600kg)=0.3m/s
KE=1/2m*v^2
KE=1/2(0.200kg+0.600kg)*(0.3m/s)^2=1/2(0.8x0.3)^2=0.036 J
state laws of refraction
Answer:
The law of refraction states that the incident ray, the refracted ray, and the normal to the interface, all lie in the same plane.
HOPE IT HELPS^_^
Answer:
There are two laws of refraction. The behavior of light as it travels through different media is described by the rules of refraction, sometimes referred to as Snell's laws. These principles control how light is affected by a barrier between two transparent materials in terms of its direction and speed.
Explanation:
First Law of refraction:- The incident ray, the refracted ray, and the normal—a line perpendicular to the boundary—all reside on the same plane according to the first law of refraction. This indicates that when light travels through a barrier between two media, its orientation changes.
Second Law of refraction:- The second law of refraction states that there is a continuous relationship between the sines of the angles of incidence and refraction (i.e., the angle between the incident ray and the normal and the angle between the refracted ray and the normal). The refractive index is a ratio that is unique to the two media in question. This may be written mathematically as:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
where n₁ and n₂ are the refractive indices of the two media, θ₁ is the angle of incidence, and θ₂ is the angle of refraction.
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Match the following
1. unit an object that orbits the Sun, is spherical, and has cleared its orbit of other large objects
2. an object that orbits the sun and is large enough for its gravity to make it spherical but that is too small to have cleared its orbit of all other large objects
3. the four inner planets; named for their rocky crusts
4.the four outer planets of the solar system; named for their high concentrations of hydrogen and helium
5. planets a unit of measurement based on the average distance of the earth from the sun; one unit equals 149.6 million kilometers
a. astronomical
b. dwarf planet
c. gas giants
d. planet
e. terrestrial
The definitions correctly match to Planet, Dwarf planet, Terrestrial, Gas giants, and Astronomical unit, respectively. These terms refer to objects and measurements relevant to astronomy and the solar system.
Explanation:
The correct matches for the given definitions are:
1. Planet - unit an object that orbits the Sun, is spherical, and has cleared its orbit of other large objects.
2. Dwarf planet - an object that orbits the sun and is large enough for its gravity to make it spherical but that is too small to have cleared its orbit of all other large objects.
3. Terrestrial - the four inner planets; named for their rocky crusts.
4. Gas giants - the four outer planets of the solar system; named for their high concentrations of hydrogen and helium.
5. Astronomical unit - a unit of measurement based on the average distance of the earth from the sun; one unit equals 149.6 million kilometers.
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What is the measure of how difficult it is for current to flow in a circult?
O A
voltage
B.
resistance
C.
power
D.
energy
Answer:
Resistance
Explanation:
Resistance "resists" the flow of electricity and makes it more difficult to travel. The higher the resistance the less current there is in a circuit. Example being, open circuit (infinity ohms) means there is no current flowing with ohms law.
A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the radius of the loop is 17.6 m, with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.
Answer:
The minimum speed must the car must be 13.13 m/s.
Explanation:
The radius of the loop is 17.6 m. We need to find the minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top.
We know that, mg be the weight of car and rider, which is equal to the centripetal force.
[tex]mg = \dfrac{mv^2}{r}\\v = \sqrt{rg}\\v = \sqrt{17.6\times 9.8}\\v = 13.13\ m/s\\[/tex]
So, the minimum speed must the car must be 13.13 m/s.
A ball rolls from x=-5 to x=32.4 m in 8.9 seconds. What was it’s average velocity
Answer:
4.157 m/s
Explanation:
Average velocity: This can be defined as the ratio change in position to time interval. The S.I unit of average velocity is m/s
The expression for average velocity is given as,
V = Δx/t.............. Equation 1
Where V = average velocity, Δx = change in position on the x- axis, t = time.
But,
Δx = x₂-x₁........... Equation 2
Substitute equation 2 into equation 1
V = (x₂-x₁)/t................ Equation 3
Given: x₂ = 32.4 m, x₁ = -5 m, t = 8.9 s
Substitute into equation 3
V = [32.4-(-5)]/8.9
V = (32.4+5)/8.9
V = 37.4/8.9
V = 4.157 m/s
Hence the average velocity = 4.157 m/s
Answer:
v = 4.20m/s
Average velocity is 4.20m/s
Explanation:
Average velocity is the change in displacement per unit time;
v = ∆x/t
Given;
∆x = 32.4 - (-5) = 37.4 m
t = 8.9 seconds
Substituting the values;
v = 37.4m/8.9s
v = 4.20m/s
Average velocity is 4.20m/s
The average intensity of light emerging from a polarizing sheet is 0.708 W/m2, and that of the horizontally polarized light incident on the sheet is 0.960 W/m2. Determine the angle that the transmission axis of the polarizing sheet makes with the horizontal.
Answer:
Angle θ = 30.82°
Explanation:
From Malus’s law, since the intensity of a wave is proportional to its amplitude squared, the intensity I of the transmitted wave is related to the incident wave by; I = I_o cos²θ
where;
I_o is the intensity of the polarized wave before passing through the filter.
In this question,
I is 0.708 W/m²
While I_o is 0.960 W/m²
Thus, plugging in these values into the equation, we have;
0.708 W/m² = 0.960 W/m² •cos²θ
Thus, cos²θ = 0.708 W/m²/0.960 W/m²
cos²θ = 0.7375
Cos θ = √0.7375
Cos θ = 0.8588
θ = Cos^(-1)0.8588
θ = 30.82°
Consider a pipe of length 80.0 cm open at both ends. What is the lowest frequency f of the sound wave produced when you blow into the pipe?
Answer:
[tex]f = 214.375\ Hz[/tex]
Explanation:
Given,
Length of the Pipe, L = 80 cm
Frequency ,f = ?
Speed of sound, v = 343 m/s
Wavelength when pipe is open at both the ends
[tex]\lambda = 2 L[/tex]
[tex]\lambda = 2\times 80 = 160\ cm = 1.6\ m[/tex]
Fundamental frequency
[tex]f =\dfrac{v}{\lambda}[/tex]
[tex]f =\dfrac{343}{1.6}[/tex]
[tex]f = 214.375\ Hz[/tex]
Final answer:
The lowest frequency produced by an 80 cm pipe open at both ends is calculated using the fundamental frequency formula for open pipes. It is found to be approximately 214 Hz, with the speed of sound at room temperature taken as 343 m/s.
Explanation:
To find the frequency, we need to consider the fundamental frequency for an open pipe, which is given by the equation f = v / (2L), where f is the frequency, v is the speed of sound in air, and L is the length of the pipe. At 20°C, the speed of sound in air is approximately 343 m/s. So, when we substitute the given values, we have:
f = 343 m/s / (2 × 0.80 m) = 214.38 Hz.
Therefore, the lowest frequency the pipe can produce, also known as the first harmonic or fundamental frequency, is approximately 214 Hz.
The 3 stages of the water cycle are
Answer:
Evaporation, condensation, precipitation
Explanation:
Answer:
Evaporation, condensation, precipitation & collection
Explanation:
What type of path does a tornado take if it touches down?
Answer:
It is very hard to predict
Explanation:
A tornado usually follows a narrow and relatively straight
path. but A tornado's path is extremely unpredictable. It could go straight, curvy, maybe even in a loop. However, a tornado will generally go in the direction of its storm.
When an object moves in a circular path, it accelerates toward the center of the circle as a result of ______.
A. terminal velocity B. momentum
C. centripetal force D. friction
Answer:
Centripetal acceleration
Explanation:
An object moving around a xirxular path maintains its route as a result of centripetal force. However, its acceleration is caused by centripetal acceleration. Despite centripetal acceleration not being among the choices, it is the right answer.
Centripetal acceleration helps an object that navigates around a circular path to accelerate while centripetal force enables the movement of an object around a circular path to move inwards. Momentum, given as one of the choices is product of mass and velocity while friction is the force opposing movement of an object around a surface.
V LESSON 4 Check
1. Classify What kind of material transmits
some light, making objects behind it appear
blurry?
Answer:
Some objects are wax paper, newspaper, and white pape
Answer:
the correct answer is Translucent
A cable-operated clutch is being adjusted. Technician A says that free travel is measured at the clutch pedal and should be between 3/4 and 1 inch (19 to 25 mm). Technician B says that the clutch spin-down time should be less than two seconds. Which technician is correct?
A) Technician A only
B) Technician B only
C) Both technicians
D) Neither technician
Answer: A
Technician A only
Explanation:
On a cable-operated clutch, the adjustment is made at the cable end. The clearance is usually measured either at the operating lever or at the pedal.
To perform efficiently, the clutch needs the right amount of play in the linkage between the foot pedal and the clutch operating lever
Anything less than the correct amount of free play (or clearance ) will result in clutch slip, because the pressure plate will be unable to exert its full pressure on the friction plate .
Failure to cure this fault will quickly lead to a burned-out friction plate, and possibly a ruined pressure plate.
What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.240 kg⋅m2, and the net force she exerts is 759 N at an effective perpendicular lever arm of 2.00 cm?
The complete question is;
To develop muscle tone, a woman lifts a 2.00-kg weight held in her hand. She uses her biceps muscle to flex the lower arm through an angle of 60.0º . What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.240 kg.m², and the net force she exerts is 759 N at an effective perpendicular lever arm of 2.00 cm?
Answer:
α = 42.76 rad/s²
Explanation:
We are given;
Mass; m = 2 kg
Distance; r = 24cm = 0.24m
Moment of inertia of the forearm; I = 0.24 kg.m²
Muscle Force; F = 759N
Perpendicular distance to lever arm; r' = 2cm = 0.02m
Angle at which she flexes arm; θ =60°
Let's assume that the arm starts extended vertically downwards. and we take the elbow joint as the point about which we calculate the torque.
Thus, we know that torque is given by the formula ;
τ = Force x Perpendicular distance
Thus, the toque exerted by force in the muscle is;
τ_muscle = 759 x 0.02 = 15.18 N.m
Also, torque exerted by the lifted weight is given as 0 because perpendicular distance is zero.
Thus, the net torque on the lower arm is;
τ_net = τ_muscle - τ_weight
τ_net = 15.18 - 0 = 15.18 N.m
Now, let's calculate moment of inertia of lifted weight.
The moment of inertia is given by;
I = mr²
Thus, moment of Inertia of lifted weight is; I_weight = 2 x 0.24² = 0.115 kg.m²
Thus,total moment of inertia is;
I_total = I_arm + I_weight
Thus, I_total = 0.24 + 0.115 = 0.355 kg.m²
Now, we can calculate the angular acceleration.
It's gotten from the equation;
τ_net = I_total•α
Where α is angular acceleration.
Thus making α the subject, we have ; α = τ_net/I_total
α = 15.18/0.355 = 42.76 rad/s²
slader A baseball player slides to a stop on level ground. Using energy consideration, calculate the distance the 65 kg baseball player slides, given his initial speed is 6 m/s and the force of friction against him is a constant 450N.
Final answer:
The 65 kg baseball player slides a distance of 5.2 meters before coming to a stop, calculated using kinetic energy and the work done by friction.
Explanation:
To calculate the distance the 65 kg baseball player slides using energy considerations, we start by noting that the work done by friction is equal to the loss in kinetic energy as the player comes to a stop. The kinetic energy (KE) of the player can be calculated using the formula KE = (1/2)mv², where m is mass and v is velocity. Since the force of friction (f) is constant, the work (W) done by friction is W = fd, with d being the distance over which the friction acts.
Setting the initial kinetic energy equal to the work done by friction, we get:
(1/2)mv² = fd
Inserting the given values, we have:
(1/2)(65 kg)(6 m/s)² = (450 N)d
Upon calculating, we find:
d = (1/2)(65 kg)(6 m/s)² / (450 N)
d = 5.2 meters
Therefore, the baseball player slides a distance of 5.2 meters before coming to a stop.
How many electrons are there in a diatomic oxygen molecule
Answer:
8 electrons
Explanation:
The bob of a simple pendulum has its maximum kinetic energy at the
Answer:
The bob of simple pendulum has its maximum kinetic energy at mean position.
Explanation:
A simple pendulum is a device which consists of mass m hanging from the string of length L attached to the some point.When displaced and released its swings back and forth with periodic motion.
The simple pendulum swings from the mean position to the extreme position and back to mean position and again the extreme position on the other side completing one oscillation.
The velocity varies with oscillation.
The velocity of bob in the extreme position is zero.
The velocity of pendulum is maximum at the mean position and hence has maximum kinetic energy because K.E =0.5 mv².
The law of conservation of energy helps us to understand it .
The height of the bob is at least when it is in the mean position, so when we move to the extreme position on the right side it is at slightly raised height and all its energy is potential energy as it is slightly motionless.As kinetic energy is zero the velocity is zero.
At mean position all energy is kinetic and velocity is maximum.
The bob of a simple pendulum has its maximum kinetic energy at the bottommost position of its swing. This is because as the pendulum swings down, potential energy is converted into kinetic energy, reaching maximum speed and maximum kinetic energy at the bottom.
Explanation:The bob of a simple pendulum has its maximum kinetic energy at the bottommost position of its swing. This is because kinetic energy is associated with the motion of the bob. When the pendulum is at its highest point (at each end of the swing), it momentarily stops and thus has no kinetic energy - instead, there's potential energy. When it falls down and reaches the bottom of its swing, or the mean position, all the potential energy is converted into kinetic energy, achieving maximum speed and thus maximum kinetic energy.
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A bird is flying directly toward a stationary bird-watcher and emits a frequency of 1420 Hz. The bird-watcher, however, hears a frequency of 1456 Hz. What is the speed of the bird, expressed as a percentage of the speed of sound
Answer:
2.47 %
Explanation:
We are given;
Frequency emitted by source(bird); f_s = 1420 Hz
Frequency heard by observer; f_o = 1456 Hz
From doppler shift frequency, we know that;
f_o = f_s [c/(c - c_s)]
Where c_s is speed of source which is the bird and c is speed of sound.
Thus;
Rearranging the equation, we have;
f_s/f_o = (c - c_s)/c
f_s/f_o = 1 - (c_s/c)
Plugging in the relevant values to get ;
1420/1456 = 1 - (c_s/c)
0.9753 = 1 - (c_s/c)
1 - 0.9753 = (c_s/c)
(c_s/c) = 0.0247
Since we want it expressed im percentage,
Thus, (c_s/c) % = 0.0247 x 100 = 2.47 %
Our local piano tuner is making a house call to tune our piano (... yes, she's maintaining social distance!) She strikes a middle C tuning fork (about 262 Hz frequency), and strikes that key on your piano. You both hear a beat frequency of about 4 Hz. What is the actual frequency of your middle C piano string
Answer:
258 Hz or 266 Hz
Explanation:
When two sounds of similar frequency occur at the same time, a phenomenon called "beat" occurs. The beat is an interference patter between the two sounds; the frequency of this beats (called beat frequency) is given by the difference between the frequencies of the two sounds:
[tex]f_B = |f_1 -f_2|[/tex]
where
[tex]f_B[/tex] is the beat frequency
[tex]f_1[/tex] is the frequency of the 1st sound
[tex]f_2[/tex] is the frequency of the 2nd sound
In this problem,
[tex]f_B=4 Hz[/tex] is the beat frequency
[tex]f_1=262 Hz[/tex] is the frequency of the middle C tuning fork
[tex]f_2[/tex] is the frequency of the middle C piano string
Solving for f2, we find two solutions:
[tex]f_2=f_1-f_B = 262-4 = 258 Hz\\f_2 = f_1+f_B = 262+4=266 Hz[/tex]