1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stellarik [79]
2 years ago
12

These two waves travel along the same string: y1 = (4.17 mm) sin(2.24?x - 300?t), y2 = (5.96 mm) sin(2.24?x - 300?t + 0.727?rad)

. What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.20 mm is also to be sent along the string in the same direction as the first two waves, what should be its phase angle in order to maximize the amplitude of the new resultant wave?
Physics
1 answer:
Luba_88 [7]2 years ago
6 0

Answer:

a) Amplitude is 9.49 mm

b) ∅ = 0.43056 rad = 24.7°

c) phase angle = 2.24x - 300t + 0.43056 rad

Explanation:

Given that;

A1 = y1 = (4.17 mm) sin(2.24x - 300t)

A2 = y2 = (5.96 mm) sin(2.24x - 300t + 0.727rad)

now phase difference between y1 and y2 is;

Δ∅ =  (2.24x - 300t + 0.727rad) - (2.24x - 300t) = 0.727 rad =  41.65°

a)  the amplitude

Amplitude A = √( A1² + A2² + 2A1A2cosΔ∅)

we substitute

A = √( (4.17)² + (5.96)² + (2 × 4.17 × 5.96 × cos(41.65) )

A = √( 17.3889 + 35.5216 + ( 49.7064 × 0.7472 )

A = √(52.9105 + 37.1406 )

A =  √90.0511

A = 9.49 mm

Therefore, Amplitude is 9.49 mm

b) the phase angle (relative to wave 1) of the resultant wave;

tan∅ = A2sinΔ∅ / ( A1 + A2cosΔ∅)

we substitute

tan∅ = 5.96sin41.65 / ( 4.17 +  5.96cos41.65)

tan∅ = 3.96088 / ( 4.17 + 4.4534)

tan∅ = 3.96088 / 8.6234

tan∅ = 0.4593

∅ = tan⁻¹ ( 0.4593 )

∅ = 0.43056 rad = 24.7°

c)

For the third wave, maximum amplitude. it should be in the direction of resultant of A1 and A2

so, phase angle in order to maximize the amplitude of the new resultant wave will be;

phase angle = 2.24x - 300t + 0.43056 rad

You might be interested in
Why is a neutral object attracted to a charged object?
mixas84 [53]
Because electricity attracts like people
7 0
3 years ago
In the first-order spectrum, maxima for two different wavelengths are separated on the screen by 3.40 mm . what is the differenc
Strike441 [17]

The solution would be like this for this specific problem:

 

Given:  

diffraction grating slits = 900 slits per centimeter

interference pattern that is observed on a screen from the grating = 2.38m

maxima for two different wavelengths = 3.40mm

 

slit separation .. d = 1/900cm = 1.11^-3cm = 1.111^-5 m <span>

Whenas n = 1, maxima (grating equation) sinθ = λ/d 
Grant distance of each maxima from centre = y .. 
<span>As sinθ ≈ y/D  y/D = λ/d λ = yd / D </span>

∆λ = (λ2 - λ1) = y2.d/D - y1.d/D 
∆λ = (d/D) [y2 -y1] 

<span>∆λ = 1.111^-5m x [3.40^-3m] / 2.38m .. .. ►∆λ = 1.587^-8 m</span></span>

6 0
3 years ago
What is a small body that follows a highly elliptical orbit around the sun
melomori [17]
A Planet, such as (pluto)
4 0
3 years ago
Read 2 more answers
A merry-go-round is shaped like a uniform disk and has moment of inertia of 50,000 kg m 2 . It is rotating so that it has an ang
lapo4ka [179]

Answer:

r = 20 m

Explanation:

The formula for the angular momentum of a rotating body is given as:

L = mvr

where,

L = Angular Momentum = 10000 kgm²/s

m = mass

v = speed = 2 m/s

r = radius of merry-go-round

Therefore,

10000 kg.m²/s = mr(2 m/s)

m r = (10000 kg.m²/s)/(2 m/s)

m r = 5000 kg.m   ------------- equation 1

Now, the moment of inertia of a solid uniform disc about its axis through its center is given as:

I = (1/2) m r²

where,

I = moment of inertia = 50000 kg.m²

Therefore,

50000 kg.m² = (1/2)(m r)(r)

using equation 1, we get:

50000 kg.m² = (1/2)(5000 kg.m)(r)

(50000 kg.m²)/(2500 kg.m) = r

<u>r = 20 m</u>

5 0
2 years ago
A 200 N trash can is pulled across the sidewalk by a person at constant speed by a force of 75 N. What is the coefficient of fri
Pavel [41]

Answer:

μ = 0.375

Explanation:

F = Applied force on the trash can = 75 N

W = weight of the trash can = 200 N

f = frictional force acting on trash can

Since the trash can moves at constant speed, force equation for the motion of can is given as

F - f = 0

75 - f = 0

f = 75 N

μ = Coefficient of friction

frictional force is given as

f = μ W

75 = μ (200)

μ = 0.375

5 0
3 years ago
Other questions:
  • Most moving objects change speed or direction at some point because _____ forces exist nearly everywhere. A. net B. normal C. ba
    12·2 answers
  • As the particles in a soup reach the bolling point what happens
    8·1 answer
  • Sphere 1 has surface area A₁ and volume V₁, sphere 2 has surface area A₂ and volume V₂. If the radius of sphere 2 is six times t
    6·1 answer
  • A car is stopped at a red light. When the light turns green, the car accelerates until it reaches a final velocity of 45 m/s. It
    11·1 answer
  • An electron in the Thomson model of hydrogen
    14·1 answer
  • A 10kg mass is moving to the right with a velocity of 15 m/s. A 13kg mass
    10·1 answer
  • What is the displacement of a person walking 20 m North, and then walks<br> 20 meters South. *
    11·1 answer
  • PLS HELP I NEED ANSWER HOMEWORK DUE SOON
    6·1 answer
  • 60 POINT!!!!!!
    6·2 answers
  • PLEAAASEE HELLPPPP?!?!?!
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!