Answer:
N₁ = 1800 turns
So, the side of the transformer that plugs into the outlet has 1800 turns.
Explanation:
The transformer turns ratio is given by the following equation:
V₁/V₂ = N₁/N₂
where,
V₁ = Voltage of outlet = 120 V
V₂ = Device Voltage = 3 V
N₁ = No. of turns on outlet side = ?
N₂ = No. of turns on side of device = 45
Therefore,
120 V/3 V = N₁/45
N₁ = (40)(45)
N₁ = 1800 turns
So, the side of the transformer that plugs into the outlet has 1800 turns.
An electron is accelerated from rest through a potential difference. After acceleration the electron has a de Broglie wavelength of 880 nm. What is the potential difference though which this electron was accelerated
Answer:
3x10⁴v
Explanation:
Using
Wavelength= h/ √(2m.Ke)
880nm = 6.6E-34/√ 2.9.1E-31 x me
Ke= 6.6E-34/880nm x 18.2E -31.
5.6E-27/18.2E-31
= 3 x 10⁴ Volts
Convert 7,348 grams to kilograms
An airplane propeller is rotating at 2200 rpm . You may want to review (Pages 255 - 259) . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Rotation of a compact disc.
A. How many seconds does it take for the propeller to turn through 49.0?
t = 4.41x10^-3 S
B. Compute the propeller's angular velocity in rad/s
w = 194 rad/s
Answer:
a) 3.7 x 10^-3 s
b) 230.41 rad/s
Explanation:
The angular speed N = 2200 rpm (revolution per minute)
==> 2200/60 revolutions per sec = 36.67 rps
The total angle turned in one second = 36.67 x 360° = 13201.2°
if it takes 1 sec to revolve 13201.2°
then it will take t sec to rotate 49.0°
time t = 49/13201.2 = 3.7 x 10^-3 s
conversion to rad/s = 2πN/60 = (2 x 3.142 x 2200)/60 = 230.41 rad/s
One solenoid is centered inside another. The outer one has a length of 54.0 cm and contains 6750 coils, while the coaxial inner solenoid is 4.00 cm long and 0.170 cm in diameter and contains 21.0 coils. The current in the outer solenoid is changing at 35.0 A/s .What is the mutual inductance of the solenoids?Find the emf induced in the inner solenoid.
Answer:
M₁₂ = 1.01 10⁻⁴ H , Fem = 3.54 10⁻³ V
Explanation:
The mutual inductance between two systems is
M₁₂ = N₂ Ф₁₂ / I₁
where N₂ is the number of turns of the inner solenoid N₂ = 21.0, i₁ the current that flows through the outer solenoid I₁ = 35.0 A / s and fi is the flux of the field of coil1 that passes through coil 2
the magnetic field of the coil1 is
B = μ₀ n I₁ = μ₀ N₁/l I₁
the flow is
Φ = B A₂
the area of the second coil is
A₂ = π d₂ / 4
Φ = μ₀ N₁ I₁ / L π d² / 4
we substitute in the first expression
M₁₂ = N₂ μ₀ N₁ / L π d² / 4
M₁₂ = μ₀ N₁ N₂ π d² / 4L
d = 0.170 cm = 0.00170 m
L = 4.00 cm = 0.00400 m
let's calculate
M₁₂ = 4π 10⁻⁷ 6750 21 π 0.0017²/ (4 0.004)
M₁₂ = π² 0.40966 10⁻⁷ / 0.004
M₁₂ = 1.01 10⁻⁴ H
The electromotive force is
Fem = - M dI₁ / dt
Fem = - 1.01 10⁻⁴ 35.0
Fem = 3.54 10⁻³ V
A 23 cm tall object is placed in front of a concave mirror with a radius of 37 cm. The distance of the object to the mirror is 86 cm. Calculate the focal length of the mirror.
Answer:
18.5 cm
Explanation:
From;
1/u + 1/v = 1/f
Where;
u= object distance = 86cm
image height = 23 cm
Radius of curvature = 37 cm
The radius of curvature (r) is the radius of the sphere of which the mirror forms a part.
Focal length (f) = radius of curvature (r)/2 = 37cm/2 = 18.5 cm
Therefore, the focal length of the mirror is 18.5 cm
You need to repair a broken fence in your yard. The hole in your fence is
around 3 meters in length and for whatever reason, the store you go to
has oddly specific width 20cm wood. Each plank of wood costs $16.20,
how much will it cost to repair your fence? (Hint: 1 meter = 100 cm) *
Answer:
cost = $ 243.00
Explanation:
This exercise must assume that it uses a complete table for each piece, we can use a direct ratio of proportions, if 1 table is 0.20 m wide, how many tables will be 3.00 m
#_tables = 3 m (1 / 0.20 m)
#_tables = 15 tables
Let's use another direct ratio, or rule of three, for cost. If a board costs $ 16.20, how much do 15 boards cost?
Cost = 15 (16.20 / 1)
cost = $ 243.00
A body is thrown vertically upwards with a speed of 95m / s and after 7s it reaches its maximum height. How fast does it reach its maximum height? What was the maximum height reached?
Explanation:
u = 95 m/sec ( Initial speed)
t = 7 sec ( Time of ascent)
According to Equations of Motion :
[tex]s = ut - \frac{1}{2} g {t}^{2} [/tex]
Max. Height = 95 * 7 - 4.9 * 49 = 424. 9 = 425 m
Answer:
332.5 m
Explanation:
At the maximum height, the velocity is 0.
Given:
v₀ = 95 m/s
v = 0 m/s
t = 7 s
Find: Δy
Δy = ½ (v + v₀) t
Δy = ½ (0 m/s + 95 m/s) (7 s)
Δy = 332.5 m
Proposed Exercises: Strength and Acceleration in Circular Movement In the situation illustrated below, a 7kg sphere is connected to a rope so that it can rotate in a vertical plane around an O axis perpendicular to the plane of the figure. When the sphere is in position A, it has a speed of 3m/s. Determine for this position the modulus of tension on the string and the rate at which the tangential velocity is increased.
Answer:
81 N
7.1 m/s²
Explanation:
Draw a free body diagram of the sphere. There are two forces:
Weight force mg pulling straight down,
and tension force T pulling up along the rope.
Sum of forces in the centripetal direction:
∑F = ma
T − mg sin 45° = m v² / r
T = m (g sin 45° + v² / r)
T = (7 kg) (10 m/s² sin 45° + (3 m/s)² / 2 m)
T = 81 N
Sum of forces in the tangential direction:
mg cos 45° = ma
a = g cos 45°
a = (10 m/s²) cos 45°
a = 7.1 m/s²
During the first part of this lab, we want to determine how the object distance is related to what two quantities
Answer and Explanation:
The computation of the object distance related to two quantities is shown below:
It could find out by using the lens formula which is shown below:
[tex]\frac{1}{v} - \frac{1}{u} = \frac{1}{f}[/tex]
where,
v = image distance
u = object distance
f = focal length
It could be found by applying the above formula i.e considering the image distance, object distance and the focal length
Now the friends are ready to tackle a homework problem. A pulse is sent traveling along a rope under a tension of 29 N whose mass per unit length abruptly changes, from 19 kg/m to 45 kg/m. The length of the rope is 2.5 m for the first section and 2.8 m for the second, and the second rope is rigidly fixed to a wall. Two pulses will eventually be detected at the origin: the pulse that was reflected from the medium discontinuity and the pulse that was originally transmitted, which hits the wall and is reflected back and transmitted through the first rope. What is the time difference, Δt, between the two pulses detected at the origin? s
Answer:
The time difference is 2.97 sec.
Explanation:
Given that,
Tension = 29 N
Mass per unit length [tex]\mu_{1}=19\ kg/m[/tex]
Mass per unit length [tex]\mu_{2}=45\ kg/m[/tex]
Length of first section = 2.5 m
Length of second section = 2.8 m
We need to total distance of first pulse
Using formula for distance
[tex]d=2.5+2.5[/tex]
[tex]d_{1}=5.0\ m[/tex]
We need to total distance of second pulse
Using formula for distance
[tex]d=2.8+2.8[/tex]
[tex]d_{2}=5.6\ m[/tex]
We need to calculate the speed of pulse in the first string
Using formula of speed
[tex]v_{1}=\sqrt{\dfrac{T}{\mu_{1}}}[/tex]
Put the value into the formula
[tex]v_{1}=\sqrt{\dfrac{29}{19}}[/tex]
[tex]v_{1}=1.24\ m/s[/tex]
We need to calculate the speed of pulse in the second string
Using formula of speed
[tex]v_{2}=\sqrt{\dfrac{T}}{\mu_{2}}}[/tex]
Put the value into the formula
[tex]v_{2}=\sqrt{\dfrac{29}{45}}[/tex]
[tex]v_{2}=0.80\ m/s[/tex]
We need to calculate the time for first pulse
Using formula of time
[tex]t_{1}=\dfrac{d_{1}}{v_{1}}[/tex]
Put the value into the formula
[tex]t_{1}=\dfrac{5.0}{1.24}[/tex]
[tex]t_{1}=4.03\ sec[/tex]
We need to calculate the time for second pulse
Using formula of time
[tex]t_{2}=\dfrac{d_{1}}{v_{1}}[/tex]
Put the value into the formula
[tex]t_{2}=\dfrac{5.6}{0.80}[/tex]
[tex]t_{2}=7\ sec[/tex]
We need to calculate the time difference
Using formula of time difference
[tex]\Delta t=t_{2}-t_{1}[/tex]
Put the value into the formula
[tex]\Delta t=7-4.03[/tex]
[tex]\Delta t=2.97\ sec[/tex]
Hence, The time difference is 2.97 sec.
How does the direction of current flow in the coil affect the orientation of the magnetic field produced by the electromagnet
Answer:
The magnetic field produced by an electric current is always oriented perpendicular to the direction of the current flow. And.Direction of magnetic field is governed by the 'right hand thumb rule, The right hand rule states that: to determine the direction of the magnetic force on a positive moving charge, ƒ, point the thumb of the right hand in the direction of v, the fingers in the direction of B, and a perpendicular to the palm points in the direction of Force . Similar to the situation with electric field lines, the greater the number of lines (or the closer they are together) in an area the stronger the magnetic field.
In a photoelectric-effect experiment it is observed that no current flows unless the wavelength is less than 540 nmnm . Part A What is the work function of this material
Answer:
Φ = 36.84 × 10^(-20) J
Explanation:
In the photoelectric effect, the energy of the incoming photon is usually used in part to extract the photoelectron from the material (work function) and then the rest is converted into kinetic energy of the photoelectron which is given by the formula;
K_max = hf - Φ
where;
hf represents the energy of the incoming photon
h is the Planck's constant
f is the light frequency
Φ is the work function of the material
K_max is the maximum kinetic energy of the photoelectrons.
From the question, we are told that no current flows unless the wavelength is less than 540 nm. This means that when the wavelength has this value, the maximum kinetic energy of the photoelectrons is zero i.e K_max = 0. Thus the energy of the incoming photons is just enough to extract the photoelectrons from the material.
Thus,
hf - Φ = 0
hf = Φ - - - (1)
We are given the wavelength as;
λ = 540 nm = 540 × 10^(-9) m
Now, let's find the frequency of the light by using the relationship between frequency and wavelength. The equation is;
f = c/λ
Where c is speed of light = 3 × 10^(8) m/s
f = (3 × 10^(8))/(540 × 10^(-9))
f = 5.56 × 10^(14) Hz
Thus, from equation 1,we can now find the work function;
Φ = hf
h is Planck's constant and has a value of 6.626 × 10^(-34) J.s
Thus;
Φ = 6.626 × 10^(-34) × 5.56 × 10^(14)
Φ = 36.84 × 10^(-20) J
Determine the final angular velocity of a particle that rotates 4500 ° in 3 seconds and an angular acceleration of 8 Rad / s ^ 2
Answer:
the final angular velocity of the particle is approximately 38.18 Rad/s
Explanation:
To start with, let's make sure that units of angle measure are the same, converting everything into radians:
[tex]4500^o\, \frac{\pi}{180^o}= 25\,\pi[/tex]
And now we can use the kinematic formulas for rotational motion:
[tex]\theta-\theta_0=\omega_0\,t+\frac{1}{2} \alpha\,t^2[/tex]
Therefore we can find the initial angular velocity [tex]\omega_0[/tex] of the particle:
[tex]\theta-\theta_0=\omega_0\,t+\frac{1}{2} \alpha\,t^2\\25\,\pi=\omega_0\,(3)+\frac{1}{2} (8)\,(3)^2\\25\,\pi-36=\omega_0\,(3)\\\omega_0=\frac{25\,\pi-36}{3} \\\omega_0\approx 14.18\,\,\,rad/s[/tex]
and now we can estimate the final angular velocity using the kinematic equation for angular velocity;
[tex]\omega=\omega_0\,+\alpha\,t\\\omega=14.18+8\,(3)\\\omega=38.18\,\,\,rad/s[/tex]
To protect her new two-wheeler, Iroda Bike
buys a length of chain. She finds that its
linear density is 0.65 lb/ft.
If she wants to keep its weight below 1.4 lb,
what length of chain is she allowed?
Answer in units of ft.
Answer:
2.2 ft
Explanation:
0.65 lb / 1 ft = 1.4 lb / x
x ≈ 2.2 ft
Coherent light with wavelength 601 nm passes through two very narrow slits, and the interference pattern is observed on a screen a distance of 3.00 m from the slits. The first-order bright fringe is a distance of 4.84 mm from the center of the central bright fringe. For what wavelength of light will thefirst-order dark fringe be observed at this same point on the screen?
Answer:
The wavelength is [tex]\lambda = 1805 nm[/tex]
Explanation:
From the question we are told that
The wavelength of the light is [tex]\lambda = 601 \ nm = 601 *10^{-9} \ m[/tex]
The distance of the screen is D = 3.0 m
The fringe width is [tex]y = 4.84 \ mm = 4.84 *10^{-3} \ m[/tex]
Generally the fringe width for a bright fringe is mathematically represented as
[tex]y = \frac{ \lambda * D }{d }[/tex]
=> [tex]d = \frac{ \lambda * D }{ y }[/tex]
=> [tex]d = \frac{ 601 *10^{-9} * 3}{ 4.84 *10^{-3 }}[/tex]
=> [tex]d = 0.000373 \ m[/tex]
Generally the fringe width for a dark fringe is mathematically represented as
[tex]y_d = [m + \frac{1}{2} ] * \frac{\lambda D }{d }[/tex]
Here m = 0 for first order dark fringe
So
[tex]y_d = [0 + \frac{1}{2} ] * \frac{\lambda D }{d }[/tex]
looking at which we see that [tex]y_d = y[/tex]
[tex]4.84 *10^{-3} = [0 + \frac{1}{2} ] * \frac{\lambda * 3 }{ 0.000373 }[/tex]
=> [tex]\lambda = 1805 *10^{-9} \ m[/tex]
=> [tex]\lambda = 1805 nm[/tex]
PLEASE HELP FAST Five-gram samples of brick and glass are at room temperature. Both samples receive equal amounts of energy due to heat flow. The specific heat capacity of brick is 0.22 cal/g°C and the specific heat capacity of glass is 0.22 cal/g°C. Which of the following statements is true? 1.The temperature of each sample will increase by the same amount. 2.The temperature of each sample will decrease by the same amount. 3.The brick will get hotter than the glass. 4.The glass will get hotter than the brick.
Answer:
1.The temperature of each sample will increase by the same amount
Explanation:
This is because, since their specific heat capacities are the same and we have the same mass of each substance, and the same amount of energy due to heat flow is supplied to both the glass and brick at room temperature, their temperatures would thereby increase by the same amount.
This is shown by the calculation below
Q = mcΔT
ΔT = Q/mc where ΔT = temperature change, Q = amount of heat, m = mass of substance and c = specific heat capacity of substance.
Since Q, m and c are the same for both substances, thus ΔT will be the same.
So, the temperature of each sample will increase by the same amount
If a ray of light traveling in the liquid has an angle of incidence at the interface of 33.0 ∘, what angle does the refracted ray in the air make with the normal?
Answer:
29°
Explanation:
because the refracted ray angle is small than angle of incidence
"Light traveling in a medium with a refractive index 1.11 is incident on a plate of another medium with index of refraction 1.66. At what angle of incidence is the reflected light fully polarized?"
Answer:
56°
Explanation:
Brewsters angle can be simply derived from
n1sin theta1= n2sintheta2= n2costheta1
because the reflected light will be 100% polarized if it is reflected at an angle 90o to the refracted light. Hence, Brewsters angle is
Tan theta= n2/n1
1.66/1.11= 1.495
Theta = 56°
Explanation:
What is the impedance of an AC series circuit that is constructed of a 10.0-W resistor along with 12.0 W inductive reactance and 7.0 W capacitive reactance
Answer:
11.2 Ω
Explanation:
The impedance of a circuit is given by;
Z= √R^2 +(XL-XC)^2
Since
Resistance R= 10 Ω
Inductive reactance XL= 12 Ω
Capacitive reactance XC= 7 Ω
Z= √10^2 + (12-7)^2
Z= √100 + 25
Z= √125
Z= 11.2 Ω
White light containing wavelengths from 410 nm to 750 nm falls on a grating with 7800 slits/cm. Part APart complete How wide is the first-order spectrum on a screen 3.20 m away
Answer:
1.227 m
Explanation:
Given that
Minimum wavelength is 410 nm
Maximum wavelength is 750 nm
Grating is 7800 slits/cm
Distance is 3.2 m
To solve this question, we would use the formula
sin θ = λ/d
sin θ = (410*10^-9) / (0.01/7800)
Sin θ = 410*10^-9 / 1.282*10^-6
Sin θ = 0.32 and θ = 18.67 degrees
For the second wavelength = 750 nm
sin θ = [(0.32x750)/410]
sin θ = (240 / 410)
sin θ = 0.5853 or
θ = 35.8 degrees
And finally, the width of spectrum would be
3.2[tan 35.8 - tan 18.67]
3.2 * 0.3833
= 1.227 m
A wire is carrying current vertically downward. What is the direction of the force due to Earth's magnetic field on the wire
Answer:
The direction of the force is towards the East.
Explanation:
Using the right hand rule, the force on the current carrying conductor is east.
In the right hand rule, if the hand is held with the fingers pointed parallel to the palm representing the magnetic field, and the thumb held at right angle to the rest of the fingers representing the direction of the current, then the palm will push in the direction of the force.
In this case, the thumb is pointing downwards, with the fingers pointing north away from the body in the direction of the earth's magnetic field, the palm will push east.
An elderly sailor is shipwrecked on a desert island but manages to save his eyeglasses. The lens for one eye has a power of 1.28 diopters, and the other lens has a power of 8.50 diopters. What is the magnifying power of the telescope he can construct with these lenses
A flat, circular loop has 18 turns. The radius of the loop is 15.0 cm and the current through the wire is 0.51 A. Determine the magnitude of the magnetic field at the center of the loop (in T).
Answer:
The magnitude of the magnetic field at the center of the loop is 3.846 x 10⁻⁵ T.
Explanation:
Given;
number of turns of the flat circular loop, N = 18 turns
radius of the loop, R = 15.0 cm = 0.15 m
current through the wire, I = 0.51 A
The magnetic field through the center of the loop is given by;
[tex]B = \frac{N\mu_o I}{2R}[/tex]
Where;
μ₀ is permeability of free space = 4π x 10⁻⁷ m/A
[tex]B = \frac{N\mu_o I}{2R} \\\\B = \frac{18*4\pi*10^{-7} *0.51}{2*0.15} \\\\B = 3.846 *10^{-5} \ T[/tex]
Therefore, the magnitude of the magnetic field at the center of the loop is 3.846 x 10⁻⁵ T.
The isotope (_90^234)Th has a half-life of 24days and decays to (_91^234)Pa. How long does it take for 90% of a sample of (_90^234)Th to decay to (_91^234)Pa?
Answer:
79.7 days
Explanation:
Half-life equation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is the amount of time,
and T is the half life.
If 90% decays, then 10% is left.
A = A₀ (½)^(t / T)
0.1 A₀ = A₀ (½)^(t / 24)
0.1 = ½^(t / 24)
ln(0.1) = (t / 24) ln(0.5)
t ≈ 79.7 days
A/An ____________________ is a small, flexible tube with a light and lens on the end that is used for examination. Question 96 options:
Answer:
"Endoscope" is the correct answer.
Explanation:
A surgical tool sometimes used visually to view the internal of either a body cavity or maybe even an empty organ like the lung, bladder, as well as stomach. There seems to be a solid or elastic tube filled with optics, a source of fiber-optic light, and sometimes even a sample, epidurals, suction tool, and perhaps other equipment for sample analysis or recovery.. Two waves that have the same wavelengths and amplitudes are traveling in opposite directions on a string. If each wave has a speed of 10 m/s and there are moments when the string is not moving, what is the wavelength of the waves if the time between each moment that the string is flat is 0.5 s?
Answer:
10m
Explanation:
Since Given frequency f= 1/t
and velocity ν=10 m/s
We know ν=λf
λ= ν/f
= 10/1/0.5
=5m
Since both the waves are similar but moves in opposite direction its total wavelength of the wave will be 10 m
In the 25 ft Space Simulator facility at NASA's Jet Propulsion Laboratory, a bank of overhead arc lamps can produce light of intensity 2500 W/m2 at the floor of the facility.
A) Find the average radiation pressure (in pascals) on a totally absorbing section of the floor.B) Find the average radiation pressure (in atmospheres) on a totally absorbing section of the floor.C) Find the average radiation pressure (in pascals) on a totally reflecting section of the floor.D) Find the average radiation pressure (in atmospheres) on a totally reflecting section of the floor.
Answer:
a) 8.33 x 10^-6 Pa
b) 8.23 x 10^-11 atm
c) 1.67 x 10^-5 Pa
d) 1.65 x 10^-10 atm
Explanation:
Intensity of the light [tex]I[/tex] = 2500 W/m^2
speed of light [tex]c[/tex] = 3 x 10^8 m/s
a) we know that the pressure for for a totally absorbing surface is given as
[tex]P_{abs}[/tex] = [tex]I/c[/tex] = 2500/(3 x 10^8) = 8.33 x 10^-6 Pa
b) 1 atm = 101325 Pa
[tex]P_{abs}[/tex] = (8.33 x 10^-6)/101325 = 8.23 x 10^-11 atm
c) for a totally reflecting surface
[tex]P_{ref}[/tex] = [tex]2I/c[/tex] = twice the value for totally absorbing
[tex]P_{ref}[/tex] = 2 x 8.33 x 10^-6 = 1.67 x 10^-5 Pa
d) 1 atm = 101325 Pa
[tex]P_{ref}[/tex] = 2 x 8.23 x 10^-11 = 1.65 x 10^-10 atm
Two sources of light of wavelength 700 nm are 9 m away from a pinhole of diameter 1.2 mm. How far apart must the sources be for their diffraction patterns to be resolved by Rayleigh's criterion
Answer:
The distance is [tex]D = 0.000712 \ m[/tex]
Explanation:
From the question we are told that
The wavelength of the light source is [tex]\lambda = 700 \ nm = 700 *10^{-9} \ m[/tex]
The distance from a pin hole is [tex]x = 9\ m[/tex]
The diameter of the pin hole is [tex]d = 1.2 \ mm = 0.0012 \ m[/tex]
Generally the distance which the light source need to be in order for their diffraction patterns to be resolved by Rayleigh's criterion is
mathematically represented as
[tex]D = \frac{1.22 \lambda }{d }[/tex]
substituting values
[tex]D = \frac{1.22 * 700 *10^{-9} }{ 0.0012 }[/tex]
[tex]D = 0.000712 \ m[/tex]
A fish is 11.9 cm from the front surface of a fish bowl of radius 33 cm. Where does the fish appear to be to someone in air viewing it from in front of the bowl
Answer:
The fish would appear 42.7 cm on the left side from the front of the bowl.
Explanation:
The fish (object) distance = 11.9 cm, radius of curvature of the bowl = 33 cm. The distance of image of the fish (image distance) can be determined by applying the mirror formula;
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{u}[/tex] + [tex]\frac{1}{v}[/tex]
where f is the focal length of the reflecting surface, u is the object distance and v is the image distance.
But, f = [tex]\frac{radius of curvature}{2}[/tex]
= [tex]\frac{33}{2}[/tex]
f = 16.5 cm
Substitute f = 16.5 = [tex]\frac{165}{10}[/tex], and u = 11.9 = [tex]\frac{119}{10}[/tex] in equation 1;
[tex]\frac{10}{165}[/tex] = [tex]\frac{10}{119}[/tex] + [tex]\frac{1}{v}[/tex]
[tex]\frac{1}{v}[/tex] = [tex]\frac{10}{165}[/tex] - [tex]\frac{10}{119}[/tex]
= [tex]\frac{1190 - 1650}{19635}[/tex]
[tex]\frac{1}{v}[/tex] = [tex]\frac{-460}{19635}[/tex]
⇒ v = [tex]\frac{19635}{-460}[/tex]
= -42.6848
v = 42.7 cm
The fish would appear 42.7 cm on the left side from the front of the bowl.
A sinusoidal sound wave moves through a medium and is described by the displacement wave function s(x, t) = 1.99 cos(15.2x − 869t) where s is in micrometers, x is in meters, and t is in seconds. (a) Find the amplitude of this wave. µm (b) Find the wavelength of this wave. cm (c) Find the speed of this wave. m/s (d) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x = 0.050 9 m at t = 2.94 ms. µm (e) Determine the maximum speed of a element's oscillatory motion. mm/s
Answer:
a) A = 1.99 μm , b) λ = 0.4134 m , c) v = 57.2 m / s , d) s = - 1,946 nm ,
e) v_max = 1,739 mm / s
Explanation:
A sound wave has the general expression
s = s₀ sin (kx - wt)
where s is the displacement, s₀ the amplitude of the wave, k the wave vector and w the angular velocity, in this exercise the expression given is
s = 1.99 sin (15.2 x - 869 t)
a) the amplitude of the wave is
A = s₀
A = 1.99 μm
b) wave spectrum is
k = 2π /λ
in the equation k = 15.2 m⁻¹
λ = 2π / k
λ = 2π / 15.2
λ = 0.4134 m
c) the speed of the wave is given by the relation
v = λ f
angular velocity and frequency are related
w = 2π f
f = w / 2π
f = 869 / 2π
f = 138.3 Hz
v = 0.4134 138.3
v = 57.2 m / s
d) To find the instantaneous velocity, we substitute the given distance and time into the equation
s = 1.99 sin (15.2 0.0509 - 869 2.94 10⁻³)
s = 1.99 sin (0.77368 - 2.55486)
remember that trigonometry functions must be in radians
s = 1.99 (-0.98895)
s = - 1,946 nm
The negative sign indicates that it shifts to the left
e) the speed of the oscillating part is
v = ds / dt)
v = - s₀(-w) cos (kx -wt)
the maximum speed occurs when the cosines is 1
v_maximo = s₀w
v_maximum = 1.99 869
v_maximo = 1739.31 μm / s
let's reduce to mm / s
v_maxio = 1739.31 miuy / s (1 mm / 103 mu)
v_max = 1,739 mm / s
a) A is = 1.99 μm , b) λ is = 0.4134 m , c) v is = 57.2 m / s , d) s is = - 1,946 nm, e) v_max is = 1,739 mm / s
Calculation of Wavelength
When A sound wave has the general expression is:
Then, s = s₀ sin (kx - wt)
Now, where s is the displacement, Then, s₀ is the amplitude of the wave, k the wave vector, and w the angular velocity, Now, in this exercise the expression given is
s is = 1.99 sin (15.2 x - 869 t)
a) When the amplitude of the wave is
A is = s₀
Thus, A = 1.99 μm
b) When the wave spectrum is
k is = 2π /λ
Now, in the equation k = 15.2 m⁻¹
Then, λ = 2π / k
After that, λ = 2π / 15.2
Thus, λ = 0.4134 m
c) When the speed of the wave is given by the relation is:
Then, v = λ f
Now, the angular velocity and frequency are related is:
w is = 2π f
Then, f = w / 2π
After that, f = 869 / 2π
Now, f = 138.3 Hz
Then, v = 0.4134 138.3
Thus, v = 57.2 m / s
d) Now, To find the instantaneous velocity, When we substitute the given distance and time into the equation
Then, s = 1.99 sin (15.2 0.0509 - 869 2.94 10⁻³)
After that, s = 1.99 sin (0.77368 - 2.55486)
Then remember that trigonometry functions must be in radians
After that, s = 1.99 (-0.98895)
Thus, s = - 1,946 nm
When The negative sign indicates that it shifts to the left
e) When the speed of the oscillating part is
Then, v = ds / dt)
Now, v = - s₀(-w) cos (kx -wt)
When the maximum speed occurs when the cosines is 1
Then, v_maximo = s₀w
After that, v_maximum = 1.99 869
v_maximo = 1739.31 μm / s
Now, let's reduce to mm / s
Then, v_maxio = 1739.31 miuy / s (1 mm / 103 mu)
Therefore, v_max = 1,739 mm / s
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