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
An LC circuit consists of a 3.4-µF capacitor and a coil with a self-inductance 0.080 H and no appreciable resistance. At t = 0 t
alexira [117]

Answer

given,

capacitance = C = 3.4-µF

inductance = L = 0.08 H

frequency is expressed as

f = \dfrac{1}{2\pi\sqrt{LC}}

time period

T = \dfrac{1}{f}=2\pi\sqrt{LC}

after time T/4 current reach maximum

 t = \dfrac{T}{4}

 t = \dfrac{2\pi\sqrt{LC}}{4}

 t = \dfrac{2\pi\sqrt{0.08 \times 3.4 \times 10^{-6}}}{4}

        t = 8.2 x 10⁻⁴ s

        t = 0.82 ms

b) using law of conservation

  \dfrac{1}{2}CV^2=\dfrac{1}{2}LI^2

  I^2 = \dfrac{CV^2}{L}

  I^2 = \dfrac{C}{L}\dfrac{Q^2}{C^2}

  I =\sqrt{\dfrac{Q^2}{CL}}

  I =\sqrt{\dfrac{(5.4 \times 10^{-6})^2}{0.08 \times 3.4 \times 10^{-6}}}

       I = 0.010 A

       I = 10 mA

4 0
3 years ago
Let w(x)=3x-7.If w(x)=14, find x
dlinn [17]

Answer:

7

Explanation:

We are given:

    w(x) = 3x   -   7

     w(x)  = 14

The problem here entails us to solve for x;

To solve for x; equate the two expressions:

         

          3x  - 7  = 14

           3x  = 14 + 7

           3x  = 21  

             x = 7

So the value of x  = 7

6 0
3 years ago
Ok these are my last points say hi if u want brainliest
lawyer [7]

Answer:

Hi

Explanation:

5 0
3 years ago
Read 2 more answers
If your Stronger than Hisoka, and you know it, Clap your hands! Oh, wait.. That’s right! You don’t have any hands. Lol
ddd [48]

Answer:

Haha pretty funny

Explanation:

3 0
2 years ago
Read 2 more answers
when in object moves stop moving changes speed or changes direction how do scientist describe that condition?
Kruka [31]

im taking test rn nd this question was on there, im saying unbalanced force, if it not correct i will put right answer, but im pretty sure the answer is unblanced

6 0
3 years ago
Read 2 more answers
Other questions:
  • A motorcycle stunt driver zooms off the end of a cliff at a speed of 30 meters per second. If he lands after 0.75 seconds, what
    11·1 answer
  • The direction of rotation of Venus is _________ to the direction of all other planets.
    9·1 answer
  • Mike is conducting an experiment in which he places several different types of soil in a funnel and then pours one liter of wate
    15·2 answers
  • Heat is distributed through the atmosphere by winds<br> True<br><br> False
    9·1 answer
  • A thin, 75.0 cm wire has a mass of 16.5 g. One end is tied to a nail, and the other is attached to a screw that can be adjusted
    7·1 answer
  • Which of the following is not a requirement of a practical fuel? A. It must occur in abundance in nature or be easy to produce.
    14·1 answer
  • Work done(as a measure of energy)=force x distance. Use this equation to show that the SI base units of energy are kg m^2 s^-2
    5·1 answer
  • Question 8: Unspooling Thread (100 points) A 110 g spool of thread with a 4.2 cm radius is held up by a peg through its center a
    13·1 answer
  • Can you plz help me please
    10·1 answer
  • A Hunter points his gun at a squirrel on a branch of a tree away from him. Assume he lies on the ground and that the moment he f
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!