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
Crazy boy [7]
3 years ago
15

In lab, your instructor generates a standing wave using a thin string of length L = 1.65 m fixed at both ends. You are told that

the standing wave is produced by the superposition of traveling and reflected waves, where the incident traveling waves propagate in the +x direction with an amplitude A = 2.45 mm and a speed vx = 10.5 m/s . The first antinode of the standing wave is a distance of x = 27.5 cm from the left end of the string, while a light bead is placed a distance of 13.8 cm to the right of the first antinode. What is the maximum transverse speed vy of the bead? Make sure to use consistent distance units in your calculations.
Given that the distance from the left end of the string to the first antinode is 27.5 cm , calculate the wavelength of the standing wave on the string. Remember to convert all measurements into units of meters before performing this calculation.
Physics
1 answer:
erik [133]3 years ago
4 0

Answer:

On the standing waves on a string, the first antinode is one-fourth of a wavelength away from the end. This means

\frac{\lambda}{4} = 0.275~m\\\lambda = 1.1~m

This means that the relation between the wavelength and the length of the string is

3\lambda/2 = L

By definition, this standing wave is at the third harmonic, n = 3.

Furthermore, the standing wave equation is as follows:

y(x,t) = (A\sin(kx))\sin(\omega t) = A\sin(\frac{\omega}{v}x)\sin(\omega t) = A\sin(\frac{2\pi f}{v}x)\sin(2\pi ft) = A\sin(\frac{2\pi}{\lambda}x)\sin(\frac{2\pi v}{\lambda}t) = (2.45\times 10^{-3})\sin(5.7x)\sin(59.94t)

The bead is placed on x = 0.138 m. The maximum velocity is where the derivative of the velocity function equals to zero.

v_y(x,t) = \frac{dy(x,t)}{dt} = \omega A\sin(kx)\cos(\omega t)\\a_y(x,t) = \frac{dv(x,t)}{dt} = -\omega^2A\sin(kx)\sin(\omega t)

a_y(x,t) = -(59.94)^2(2.45\times 10^{-3})\sin((5.7)(0.138))\sin(59.94t) = 0

For this equation to be equal to zero, sin(59.94t) = 0. So,

59.94t = \pi\\t = \pi/59.94 = 0.0524~s

This is the time when the velocity is maximum. So, the maximum velocity can be found by plugging this time into the velocity function:

v_y(x=0.138,t=0.0524) = (59.94)(2.45\times 10^{-3})\sin((5.7)(0.138))\cos((59.94)(0.0524)) = 0.002~m/s

You might be interested in
If the car went 30 km west in 25 min. and then 40 km east in 35 min., what would be its total displacement?
Mandarinka [93]
The total displacement is 10 km.
8 0
3 years ago
A car travels 45 km due north and 70 km west. What is the car's displacement? 6 points 24.7 km northeast 83.2 km northwest 76.5
HACTEHA [7]

Answer:

3150

Explanation:

if if you were two times 45 times 70 it would give you that answer

8 0
3 years ago
The energy that generates wind comes from what source?
Rudiy27

Answer:

we can say that wind energy is due to

D) Severe thunderstorms

Explanation:

As we know that wind energy is converted into kinetic energy of wind mills

This kinetic energy of wind mill is then converted into electrical energy using turbine

now we can consider here  energy conservation theory that energy is only converted from one form to other form

it neither be destroyed nor be created but it can transfer from one form to other form

So here we can say that wind energy is due to

D) Severe thunderstorms

3 0
3 years ago
1. What causes velocity to change?
tresset_1 [31]
The amount of force an object has will change the velocity
4 0
3 years ago
Read 2 more answers
Distributions of electric charges in a cell play a role in moving ions into and out of a cell. In this situation, the motion of
Y_Kistochka [10]

Answer:

An atom is the smallest constituent unit of ordinary matter that constitutes a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small; typical sizes are around 100 picometers.Explanation:

7 0
3 years ago
Other questions:
  • Officials begin to release water from a full man-made lake at a rate that would empty the lake in 4 weeks, but a river that can
    11·1 answer
  • if you have an isotope of the element carbon (C) that has the mass number of 14, what other information would help you determine
    12·1 answer
  • Which kingdom<br> does the owl belong to
    11·1 answer
  • Which term is defined as long chains of carbon molecules?
    15·2 answers
  • How many magnitude 8 earthquakes does it take to equal the energy release for a magnitude 9 earthquake?
    14·1 answer
  • (c) What is electricity? Write its any two uses​
    12·1 answer
  • Why would scientists call solids and liquids a condensed phase of matter?
    8·1 answer
  • In separate experiments, a large number of particles (all with the same charge, but with a wide variety of masses and speeds) ar
    9·1 answer
  • Who yall think gonna win Seahawks or Vikings? Seahawks all the way
    14·2 answers
  • How do you calculate the total pressure?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!