The sound intensity of a jet engine radiating an acoustic power of 2.11×105 w sound at a distance of 50.3 m from the engine is approximately 6.64 [tex]W/m^2[/tex].
The intensity means the amount of loudness in it. The actual definition of intensity is the amount of power a sound has per unit area.
Mathematically, the intensity can be written as:
[tex]I=\frac{Power}{Area}[/tex]
The given data:
Power, P = [tex]2.11\times 10^5 W[/tex]
Area, A = [tex]4\pi d^2=4\pi (50.3)^2 m^2[/tex]
So using the formula, we have:
[tex]I=\frac{2.11\times 10^5}{4\pi (50.3)^2} \approx 6.64 W/m^2[/tex]
Hence, the intensity of a jet engine is approximately 6.64 [tex]W/m^2[/tex].
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how high would the atmosphere extend if it were of uniform density throughout. equal to half the present density at sea level?
The height the atmosphere would extend is 16,218.5 m.
What is air pressure at sea level?
The standard atmospheric pressure at sea level has a magnitude of 101,325 N/m².
Pa = ρgh
where;
Pa is the atmospheric pressure = 101,325 Paρ is density of air = 1.275 kg/m³h is height = ?g is acceleration due to gravity = 9.8 m/s²when the density of air is half, ρ = 0.5ρ
Pa = (0.5ρ)gh
h = Pa/(0.5ρg)
h = (101,325) / (0.5 x 1.275 x 9.8)
h = 16,218.5 m
Thus, the height the atmosphere would extend is 16,218.5 m.
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An inductor that has an inductance of 15.0H and a resistance of 30.0Ω is connected across a 100-V battery. What is the rate of increase of the current(b) at t=1.50s ?
The rate of increase of the current in the given circuit is determined as 6.67 A/s.
Rate of current increase
The rate at which the current increases is calculated as follows;
E = L(di/dt)
where;
E is the emf of the batteryL is the inductance of the inductordi/dt is rate of change of currentThe rate of increase of the current is calculated as follows;
di/dt = E/L
di/dt = 100 / 15
di/dt = 6.67 A/s
Thus, the rate of increase of the current in the given circuit is determined as 6.67 A/s.
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imagine that distance d is much greater than the length of the wire. intuitively, what should the magnitude of the electric field at point p be in this case? express your answer in terms of some or all of the variables q and d , and the constants π and ϵ0 . the variable l should not appear in your answer. view available hint(s)
If the distance d is much greater than the length of the wire, then intuitively, the magnitude of the electric field at point p should be very large. This is because a strong electric field will cause an increase in current flow through any metal conductor. In this case, due to how greater d is compared to l, there would likely be a significant amount of electricity flowing through both wire and ground.
It will happen as a result of a stronger field and more room between charges. In order to determine this magnitude, one method is to apply Coulomb's Law, which stipulates that:
E=q×C where,
E is the electric field.
q is charge per unit area.
C is the amount of charge held by a object.
How can Coulomb's law be derived?Coulomb's law can be derived from the principle of electrostatics. This states that an electrical force is equal and opposite to the electric field at any point in space. In other words, if you charge a capacitor up with electricity, the voltages on each terminal will oppose one another and cause a Force between them (Coulomb's Law).
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an object which has a mass of 70 kg is sitting on a cliff 10 m high. calculate the object's potential energy. given g
An object which has a mass of 70 kg is sitting on a cliff 10 m high. the object's potential energy is 7,000 J
Given: m = 70 kg in mass Height h = 10 m and acceleration g = 10 m/s2
Required. Potential Energy of Gravitation, or P.E
Equation: P.E = mgh
= (70 Kg)(10 m/s²) ( 10 m)
P.E. equals 7,000 kg/m2 or
P.E = 7,000 J
Why is potential energy called that?Scottish physicist William Rankine initially used the word "potential energy" in the 19th century, and it has since become a cornerstone of the science. Because of their location, which makes them position relative, items that have this energy stored in them have the capacity to unleash it.
Our knowledge of the cosmos and how we fit into it depends on potential energy. In fact, potential energy and the labour necessary to move an item are determined by the position of the object in the universe.
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a piece of ice at 0 degree cools in a drink more effectively than the same mass of water at the same temperature
Answer:
Drinks are cooled more effectively by ice pieces at 00C and not by water at 00C. This is because ice takes away more heat from the drink while melting as a result of high specific latent heat capacity of ice.
Explanation:
GP Submarine A travels horizontally at 11.0 m/s through ocean water. It emits a sonar signal of frequency f = 5.27× 10³Hz in the forward direction. Submarine B is in front of submarine A and traveling at 3.00 m/s relative to the water in the same direction as submarine A. A crewman in submarine B uses his equipment to detect the sound waves ("pings") from submarine A. We wish to determine what is heard by the crewman in submarine B. (c) In Equation 17.19 , should the sign of v(O) be positive or negative?
The sign of v(O) is positive.
What is frequency in physics?Recurrence is the quantity of events of a rehashing occasion for each unit of time. It is additionally once in a while alluded to as fleeting recurrence to underscore the difference to spatial recurrence, and customary recurrence to stress the differentiation to precise recurrence. Recurrence is communicated in units of hertz (Hz) which is comparable to one (occasion) each second. The comparing time frame is the time term of one cycle in a rehashing occasion, so the period is the corresponding of the recurrence. Recurrence is estimated in units called hertz (Hz). At the point when one wave passes in a single second its recurrence is 1 wave each second or 1 Hertz. Recurrence and period are really alternate extremes. While period is estimated in seconds per cycle, recurrence is estimated in cycles each second. Think about our wave with a time of 2 seconds.
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The most soaring vocal melody is in Johann Sebastian Bach's Mass in B Minor. In one section, the basses, tenors, altos, and sopranos carry the melody from a low D to a high
A. In concert pitch, these notes are now assigned frequencies of 146.8Hz and 880.0 Hz . Find the wavelengths of(c) the initial note and
The wavelength of the initial note is 2.34m
What do you mean by the term wavelength?The distance between two successive crests or troughs of a wave is known as its wavelength. It is measured in the wave's direction. The distance a wave travels between its crests or troughs is known as its wavelength (which may be an electromagnetic wave, a sound wave, or any other wave). The wave's crest is its highest point, while its dip is its lowest. Because a wavelength represents a distance or length, it is expressed in length units like meters, centimeters, millimeters, nanometers, etc. Light's wavelength changes with color, or it differs for each hue. While violet has the shortest wavelength, red has the longest.
wavelength = v/f
Given:
Initial frequency, [tex]f_{initial} = 146.8 Hz[/tex]
Final frequency, [tex]f_{final} = 880\;Hz[/tex]
Sound Level, [tex]\beta = 79\;dB[/tex]
We know that,
Speed of the sound, [tex]v=343\;m/s[/tex]
Density of air, [tex]\rho=1.2\;kg/m^{3}[/tex]
Wavelength, [tex]\lambda = \frac{v}{f}[/tex]
Wavelength of initial note is,
[tex]\lambda = \frac{v}{f_{initial} }[/tex]
Substitute the known values in the above equation,
[tex]\lambda = \frac{343}{146.8}[/tex]
[tex]\lambda = 2.34\;m[/tex]
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If the photoelectric effect is observed for one metal, can you conclude that the effect will also be observed for another metal under the same conditions? Explain.
No, we cannot conclude that the photoelectric effect will also occur for different metals under the same conditions.
The photoelectric effect is a phenomenon in which electrons are ejected from the surface of a metal when light hits it. This emitted electron is called a photoelectron. The photoelectric effect occurs because electrons on a metal surface tend to absorb energy from incident light, thereby overcoming the attractive force that binds the electrons to the metal core.Mathematically , we can define the photoelectric effect as:
[tex]K.E_m_a_x=E-\phi[/tex]
where [tex]K.E_m_a_x[/tex] is the kinetic energy of the free electron, E is the energy of the incident photon, and Ф is the work function, the energy needed to release the electron from its parent atom.
For example if we take a light of 2eV that is incident on cesium, which has a work function of 1.26 eV. In this case, since the photon energy is greater than the work function, an electron can be emitted.
but if we hit this light of 2eV on the platinum which has a work function of 3.65eV . Apparently, this time the light doesn't have enough energy to free loosely bound electrons from their parent atoms.
Thus ,the emission of photoelectrons and the kinetic energy of the emitted photoelectrons depend on the frequency of light incident on the metal surface.
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If it takes my car 2.2 seconds to accelerate from 8.9 m/s to 35.76 m/s, what is my cars average acceleration in that time?
A -1 2.2 m/s2
B 12.2 m/s2
C 0 m/s2
D 26.86 m/s2
what is the magnitude of the force (in newtons) exerted on a charge 1.4 mc by an electric field 211.1 n/c that points due east? your answer should be a number with four decimal places, do not include the unit.
The magnitude of the force is 295.54 x 10⁻³ N
Attraction betweem nucleus and electron is by electric force. Now, a positive or negative charge generates a field in the void surrounding it. We refer to this void as the electric field.
We know that , force can be found out by given formula
F = q × E where,
F = Force
q = Charge
E = Electric field
Here, the direction of Force is the same as that of the Electric field
Substituting the values, we get
F = 1.4 x 10⁻³ x 211.1
=295.54 x 10⁻³ N
Thus, the magnitude of force is 295.54 x 10⁻³ N
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A nonconducting sphere has mass 80.0 g and radius 20.0cm . A flat, compact coil of wire with five turns is wrapped tightly around it, with each turn concentric with the sphere. The sphere is placed on an inclined plane that slopes downward to the left (Fig. P29.65), making an angle Ф with the horizontal so that the coil is parallel to the inclined plane. A uniform magnetic field of 0.35T vertically upward exists in the region of the sphere.(b) Show that the result does not depend on the value of Ф .
The torque value is 560 Nm, so the result does not depend on the value of Ф.
Given:
Mass=80.0 g
Radius=20.0 cm
Magnetic field=0.35T
In a magnetic field, a loop of current-carrying wire will experience the following torque:
τ=μ×Β
Here, is the μ magnetic moment and Β is the magnetic field.
τ= 1600 × 0.35 T
τ= 560 Nm
What is torque and its SI unit?The rotating equivalent of force is torque. It is also known as the moment, moment of force, rotating force, or turning effect depending on the field of research. It serves as an example of how a force can alter a body's rotational motion.
The Newton-metre, or kgm2sec-2, is the SI unit for torque. How did we get to this point? Considering the equation Torque = Force X Distance Torque is measured in newton-meters, whereas distance is measured in meters and force is measured in newtons.
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a force vector f has a magnitude of 12.0 n. it is oriented 60° to the left of the y ax what are its x and y components?
The force vector that has a magnitude of 12.0 N. and is oriented 60° to the left of the (y) has the followings components:
v(x) =6 Nv(y) = 10.39 NTo solve this exercise the formulas and procedures we will use are:
v(x) = v * cosine (angle)v(y) = v * sine (angle).Where:
v= magnitude of the vectorv(x) = component of the vector on the (x) axisv(y) = component of the vector on the (y) axisangle = angleInformation about the problem:
angle = 60ºv = 12.0 Nv(x)= ?v(y)= ?Applying the formula of the component of the vector in the (x) axis we have:
v(x) = v * cosine (angle).
v(x) = 12.0 N * cosine (60º)
v(x) =6 N
Applying the formula of the component of the vector in the (y) axis we have:
v(y) = v * sine (angle)
v(y) = 12.0 N * sine (60º)
v(y) = 10.39 N
What is a vector?It can be said to be a straight line described by a point (a) and (b) that has direction and sense.
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at 8pm, you see that the pointer stars of the big dipper and the star polaris are arranged in a vertical line. how long, give or take a few minutes, would you need to wait to see them arranged in a horizontal line?
6 hours long, give or take a few minutes, you need to wait to see them arranged in a horizontal line if, at 8 pm, you see that the pointer stars of the big dipper and the star Polaris are arranged in a vertical line.
What do you mean by pointer star?The two prominent stars in Ursa Major known as the Pointer Stars can be utilized to locate Polaris, the North Star. The Big Dipper asterism includes the two stars Dubhe and Merak (Alpha and Beta Ursae Majoris). They trace the bowl of the Dipper's exterior. The direction of the North Star is indicated with a line that runs from Merak via Dubhe. Because it identifies the location of the celestial north pole, Polaris is significant in navigation. While other stars and constellations seem to revolve around it, the star is constantly found in the same location in the sky throughout the year.
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robert uses a spring scale to measure force. what is the unit of his measurement? joules joules newtons newtons volts volts pascals
Robert uses a spring scale to measure force. The unit of his measurement is newtons.
What is force?In material science, a power is an impact that can change the movement of an item. A power can make an item with mass change its speed, i.e., to speed up. Power can likewise be portrayed naturally as a push or a force. Logicians in classical times involved the idea of power in the investigation of fixed and moving articles and basic machines, yet scholars, for example, Aristotle and Archimedes held crucial mistakes in grasping power. To a limited extent this was because of a deficient comprehension of the occasionally non-clear power of erosion, and a thusly lacking perspective on the idea of normal movement.
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characterizing vibration-assisted atomic force microscopy (afm)-based nanomachining via perception of acoustic emission phenomena using a sensor-based real-time monitoring approach
The study 'characterizing vibration-assisted atomic force based nanomachining' aims to elucidate nanomachine properties for heterogeneous materials.
What is nanomachining?The expression nanomachining makes reference to the study of nanometric machines (nanomachines) and related materials, which can be achieved by different approaches including sensor-based strategies related to acoustic auditive phenomena.
In conclusion, the study 'characterizing vibration-assisted atomic force based nanomachining' aims to elucidate nanomachine properties for heterogeneous materials.
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Calculate the speed of a car at the 10th s, the car accelerates at
6m/S2 from a position of rest.
Answer:
Do you have the fomular send please so I can work on it
When the volume of gas in the syringe was 45 cm3, the pressure gauge showed a value of 60 kPa.
Calculate the pressure in the gas when the volume of gas in the syringe was 40 cm3.
The Pressure of gas in the syringe when at an initial pressure of 60 kPa and when the volume decreased from 45 cm³ to 40 cm³ is 67.5 kPa.
What is pressure?Pressure can be defined as the force acting perperdicular per unit area to the surface of an object.
To calculate the pressure in the gas, we use the formula below
Formula:
PV = P'V'............ Equation 1Where:
P = Initial pressureV = Initial volumeP' = Final pressureV' = Final volume.Make P' the subject of the equation
P' = PV/V'........... Equation 2From the question,
Given:
P = 60 kPaV = 45 cm³V' = 40 cm³Substitute these values into equation 2
P' = (60×45)/40P' = 67.5 kPaHence, the pressure of the gas is 67.5 kPa.
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Why is the following situation impossible? At the Summer Olympics, an athlete runs at a constant speed down a straight track while a spectator near the edge of the track blows a note on a horn with a fixed frequency. When the athlete passes the horn, she hears the frequency of the horn fall by the musical interval called a minor third. That is, the frequency she hears drops to five-sixths its original value.
Achieving a speed of 112.25 km/h is impossible for a human.
What do you mean by frequency?The frequency of an event is its repetitions per unit of time. In a contrast to spatial frequency, it is also sometimes referred to as temporal frequency. Hertz (Hz), which equals one (event) per second, is the unit of frequency. The reciprocal of frequency is period, which is defined as the length of time for one cycle of a repeating occurrence.
According to the question:
Emitted frequency, f₀
Frequency heard when athlete approaches horn, f₁
Frequency heard when the athlete passes horn, f₂
Speed of the athlete (observer), v₁
Speed of sound in air = 343m/s
When an athlete approaches the horn, the frequency observed is given by,
f₁=( (v+v₁)/(v-v₂) ) ₓ f₀
f₂=( (v-v₁)/(v-v₂) ) ₓ f₀
From question,
f₂/f₁ = 5/6
5/6 = v-v₁/v+v₁
hence, v₁ = 112.25 km/h
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The accompanying table shows measurements of the Hall voltage and corresponding magnetic field for a probe used to measure magnetic fields. (b) If the measurements were taken with a current of 0.200 A and the sample is made from a material having a charge-carrier density of 1.00×10²⁶ carriers/m³, what is the thickness of the sample?
0.125 mm . is the thickness of the sample.
What do you mean by hall voltage ?The Hall effect is the creation of a voltage difference (the Hall voltage) across an electrical conductor, which is transverse to an applied magnetic field perpendicular to the current and an electric current in the conductor. Edwin Hall made the discovery in 1879.
We need to know the material's current, magnetic field, length, number of charge carriers, and area in order to calculate the Hall voltage. The Hall voltage is computed using the formula: v=IBlneA=(100A)(1.5T)(1.0102m)(5.91028/m3)(1.61019C)(2.0105m2)=7.9106V.
lof4
First we have to plot those point Then we can use some computer program to fit those point linearly to get slope
of that graph a and interception b. We already know, from theory, that Hall's voltage AVH and magnitude of
magnetic field B are connected as
Δ[tex]V_{H} =\frac{I}{nqt} B[/tex]
where I is current trough probe, n is concentration of charge carriers, q = 1.6 • 10¯19 C is charge of charge
carries and t is thickness of the material. We have put the data from the problem on a graph and fitted linearly and
got
a = 100 μ[tex]\frac{V}{T}[/tex]
b = —0.02 μV.
As we can see, our result are in agreement with theoretical assumptions because interception b is almost O, and a
is asked relation between Hall's voltage A VH and magnitude of magnetic field B. Then we can write
ΔVH =[tex]100X10^{-6}[/tex] V/TB
(4) Then we can use result (4) and numbers from the textbook to calculate the thickness of the sample as
[tex]a=\frac{I}{nqt} \\t=\frac{I}{anq} \\t=\frac{.200A}{100X10^{-6}X 1.6 X10^{-19}X10^{26} } \\t=0.125mm[/tex]
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A particle with electric charge q moves along a straight line in a uniform electric field →E with speed u . The electric force exerted on the charge is qE . The velocity of the particle and the electric field are both in the x direction.(b) Discuss the significance of the dependence of the acceleration on the speed.
A physical field called an electric field surrounds electrically charged particles and attracts or repels all other charged particles nearby. The physical field of a system of charged particles can also be referred to as the electric field.
In a uniform electric field E, a particle with electric charge q moves in a straight line. The speed of the particle is u.
The electric force exerted in the charge is qE.
The electric field and the velocity of the particle are both in the x direction.
For a small speed u when compared to the speed of light c, the relativistic equation reduces to the classical acceleration:
a = qE / m
Now, as u approaches c, the acceleration will tend to zero, so that the object can or will never reach the speed of light.
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A wave has a wavelength of 2.5 m and a frequency of 150 Hz. What is its speed? (Note: c= f)
380 m/s
200 m/s
60 m/s
500 m/s
If a wave has a wavelength of 2.5 m and a frequency of 150 Hz, then the speed of the wave would be
What is Wavelength?It can be understood in terms of the distance between any two similar successive points across any wave for example wavelength can be calculated by measuring the distance between any two successive crests.
As given in the problem If a wave has a wavelength of 2.5 m and a frequency of 150 Hz, then we have to find the speed of the wave,
The speed of the wave = frequency of the wave × wavelength
= 150 × 2.5
=375 meters / seconds
Thus, the speed of the wave would be 375 meters / seconds.
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A long, straight metal rod has a radius of 5.00cm and a charge per unit length of 30.0nC/m . Find the electric field (b) 10.0cm
The electric field is 5.39 × 10^3 N/C.
R(radius of the metal rod) = (10cm)( 1m/100cm) = 0.1m
[tex]\lambda\;(\text{charge per unit length})=(30\;\mathrm{nC/m})\left(\dfrac{1\;\mathrm{C}}{10^9\;\mathrm{nC}} \right)=\textcolor{#ff9c8c}{30\times 10^{-9}\;\mathrm{C/m}}[/tex]
Since the rod is long L≫l, we model it as a long filament of infinite length and constant charge per unit length for which the electric field is found from Equation (*):
[tex]E=\dfrac{\lambda}{2\pi \epsilon_0 r} \\[/tex]
Substitute numerical values:
[tex]E&=\dfrac{30\times 10^{-9}}{2\pi (8.8542\times 10^{-12})(0.1)}\\ &={5.39\times 10^{3}\;\mathrm{N/C}}}[/tex]
electric field, an electric property associated with each point in space when the charge is present in any form. The magnitude and direction of the electric field are expressed by the value of E, called electric field strength or electric field intensity or simply the electric field.
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anyone know what it is?
The scientific experiments are performed under controlled conditions, which can be considered characteristic of science, therefore the correct answer is option C.
What is science?The deliberate, empirically supported pursuit and application of knowledge and understanding of the natural and social worlds are what is known as science.
Science is characterized by the controlled environments in which experiments and observations are made.
Thus, option C is the proper response.
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It takes an airplane 9 hours to fly from Santiago, Chile to Miami at a speed of 480 km/h. What is the distance travelled by the airplane from Santiago to Miami?
a) 4,320 km
b) 4,800 km
c) 3,240 km
d) 5,333 km
The legal highway speed limit in colorado is 75 miles per hour. What is this in kilometers per hour?
In a certain experiment, a filament in an evacuated lightbulb carries a current I₁ and you measure the spectrum of light emitted by the filament, which behaves as a black body at temperature T₁ . The wavelength emitted with highest intensity (symbolized by λmax) has the value λ₁ . You then increase the potential difference across the filament by a factor of 8 , and the current increases by a factor of 2 .(i) After this change, what is the new value of the tempera-(ii) What is the new value of the wavelength emitted with highest intensity? (a) 4 λ₁ (b) 2λ₁ (c) λ₁ (d) 1/2 λ₁ (e) 1/4 λ₁
The new value of the temperature is T₂ = 2T₁ and the new value of the wavelength with the highest intensity is λ₂ = (1/2) λ₁.
Using Stefan's equation, which states that the power of the emitted radiation will be proportional to the fourth power of the absolute temperature, we treat the filament of the evacuated light bulb as a black body.
P = σ AeT⁴
Where Ais the surface area of the emitter, σ is Stefan's constant, and e is the emissivity of the surface.
Now, from Stefan's Law, the radiated power is proportional to the fourth power of temperature.
P =IV
IV ∝ T⁴
Therefore,
I₁ V₁ / (I₂ V₂) = (T₁ / T₂)⁴
T₁ / T₂ = (I₁ V₁ / I₂ V₂)^{1/4}
T₂ = T₂ [ (I₁ V₁ / I₂ V₂)^{1/4} ]
Now we have,
I₂ = 2I₁ and
V₂ = 8V₁
Therefore,
T₂ = T₁ [ (2I₁ )(8V₁)/(I₁ V₁) ]^{1/4}
T₂ = T₁ (16)^{1/4}
T₂ = 2T₁
Let λ₁ be the wavelength emitted with the highest intensity initially and λ₂ be the wavelength emitted with the highest intensity after the change.
Then by Wiens law:
λ₁ T₁ = λ₂ T₂
λ₁ T₁ = λ₂ (2T₁)
λ₂ = (1/2) λ₁
Therefore, the new value of the wavelength is 1/2 λ₁.
The correct option is (d).
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a very small magnet is wound with 97 layers with 215 turns per layer. how many turns of wire are on the coil?
20855 turns of wire are on the coil.
What do you mean by a magnet?A substance or thing that creates a magnetic field is called a magnet. The most noteworthy characteristic of a magnet—a force that pulls on other ferromagnetic elements, such as iron, steel, nickel, cobalt, etc.—as well as the ability to attract or repel other magnets—is caused by this invisible magnetic field. An object made of a substance that has been magnetized and produces its own persistent magnetic field is referred to as a permanent magnet. A common example is a refrigerator magnet used to keep notes on the door of the refrigerator. Ferromagnetic materials are those that can be magnetized and are also those that are powerfully drawn to a magnet (or ferrimagnetic).
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a student solving a physics problem to find the unknown has applied physics principles and obtained the expression: μkmgcosθ
The physics problem to find the unknown has applied physics principles will be the following:
The simplified expression for coefficient of kinetic friction is 0.097.
The given parameters:
g = 9.8 m/s²
a = 3.6 m/s²
θ=27.0∘
The simplified expression for coefficient of kinetic friction is calculated as follows;
μkmgcosθ = mgsinθ − ma
m(μkgcosθ) = m(gsinθ − a)
μkgcosθ = gsinθ − a
The practise of using physics as a science to assist people and address their issues is known as applied physics.
Engineering is distinct from it since engineers deal with clearly defined problems. Applying physics to the development of new technologies or the resolution of engineering issues is the work of applied physicists.
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A string of length L , mass per unit length μ, and tension T is vibrating at its fundamental frequency. (ii) If the mass per unit length is doubled, with all other factors held constant, what is the effect on the fundamental frequency? Choose from the same possibilities as in part (i).
Fundamental frequency will be [tex]\frac{1}{\sqrt{2} }[/tex] times that of original frequency on doubling the mass per unit length.
Fundamental frequency, also called simply fundamental wave, is defined as the lowest frequency of a periodic waveform. In music, the root is the pitch of the note that is perceived as the lowest partial present.A wave traveling on the string is reflected at the other end. Standing waves are created as a result of interference between incident and reflected waves propagating in opposite directions. The fundamental frequency of the standing wave of a taut string is given by [tex]f=\frac{1}{2l} \sqrt{\frac{T}{u} }[/tex] ....(1) where T is the tension in the string, u is the mass per unit length of the string , l is the length of the string.From equation (1) , it can be seen clearly that fundamental frequency is inversely proportional to the square root of the mass per unit length of the string.
On putting double the mass per unit length in equation (1) keeping the all factor same , we get
[tex]f'=\frac{1}{2l} \sqrt{\frac{T}{2u} }\\\\f'=\frac{1}{\sqrt{2} } f[/tex]
Where f ' is the new frequency and f is the original frequency .
Thus, on doubling the mass per unit length, with all other factors held constant then the fundamental frequency will be [tex]\frac{1}{\sqrt{2} }[/tex] times that of original frequency.
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A 4.00×100-g glass coffee cup is 20.0°C at room temperature. It is then plunged into hot dishwater at a temperature of 80.0°C, as shown in Figure 12-18. If the temperature of the cup reaches that of the dishwater, how much heat does the cup absorb? Assume that the mass of the dishwater is large enough so that its temperature does not change appreciably.
The amount of heat the cup absorb is 1003200 J.
Given,
Mass of coffee cup = 4.00 × 100 g or 4 kg
Room temperature = 20°C
Hot water temperature = 80°C
We have to find the amount of heat the cup absorbed.
Now, by using the specific heat formula, we have
Q = mCΔT
Where m is the mass of the substance, c is the specific heat, ΔT is the change in temperature, and Q is the amount of heat received or lost.
Putting the values, we get
Q = 4 × 4180 × (80°- 20°)
Q = 1003200 J/kg K
Hence, the amount of heat absorbed by the cup is 1003200 J/kg K.
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