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
anastassius [24]
3 years ago
9

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating i

n its third OVERTONE, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m-1)x] cos[(166 rad/s)t]. (a) What are the frequency and wavelength of the fundamental mode of this string? (b) How long is the string? (c) How fast do waves travel on this string?
Physics
1 answer:
Fofino [41]3 years ago
4 0

Answer:

(a) Wavelength is 0.436 m

(b) Length is 0.872 m

(c) 11.518 m/s

Solution:

As per the question:

The eqn of the displacement is given by:

y(x, t) = (1.22 cm)sin[14.4 m^{- 1}x]cos[(166\ rad/s)t]          (1)

n = 4

Now,

We know the standard eqn is given by:

y = AsinKxcos\omega t           (2)

Now, on comparing eqn (1) and (2):

A = 1.22 cm

K = 14.4 m^{- 1}

\omega = 166\ rad/s

where

A = Amplitude

K = Propagation constant

\omega = angular velocity

Now, to calculate the string's wavelength,

(a) K = \frac{2\pi}{\lambda}

where

K = propagation vector

\lambda = \frac{2\pi}{K}

\lambda = \frac{2\pi}{14.4} = 0.436\ m

(b) The length of the string is given by:

l = \frac{n\lambda}{2}

l = \frac{4\times 0.436}{2} = 0.872\ m

(c)  Now, we first find the frequency of the wave:

\omega = 2\pi f

f = \frac{\omega}{2\pi}

f = \frac{2\pi}{166} = 26.42\ Hz

Now,

Speed of the wave is given by:

v = f\lambda

v = 26.419\times 0.436 = 11.518\ m/s

You might be interested in
Describe seven physical properties that help distin-<br> guish one mineral from another.
Lilit [14]

Answer:

Color, Streak, luster, cleavage and fracture, hardness, crystal shape, and density.

Explanation:

6 0
3 years ago
What is the slope of the line?
coldgirl [10]
(30, 5)
(10, 1)

change of y / change of x
= (30 - 10) / (5 - 1)
= 20 /4
= 5
6 0
3 years ago
Determine the magnitude of the effective value of g⃗ at a latitude of 60 ∘ on the earth. assume the earth is a rotating sphere.
dezoksy [38]
In addition to acceleration of gravity we experience centrifugal acceleration away from the axis of rotation of the earth. this additional acceleration has value ac = r w^2 where w = angular velocity and r is distance from your spot on earth to the earth's axis of rotation so r = R cos(l) where l = 60 deg is the lattitude and R the earth's radius and w = 1 / (24hr x 3600sec/hr) 
<span>now you look up R and calculate ac then you combine the centrifugal acc. vector ac with the gravitational acceleration vector ag = G Me/R^2 to get effective ag' = ag -</span>
5 0
3 years ago
A force of 2 kN is applied to an object to make it move 3.6 m in the direction of the force. Select the correct value of work do
vaieri [72.5K]

Answer:

W= F × d

W= 2kn × 3.6

W= 7.2 J

Work is measured in Joules!

4 0
3 years ago
A spherical gas-storage tank with an inside diameter of 9 m is being constructed to store gas under an internal pressure of 1.50
lutik1710 [3]

Answer: 33 mm

Explanation:

Given

Diameter of the tank, d = 9 m, so that, radius = d/2 = 9/2 = 4.5 m

Internal pressure of gas, P(i) = 1.5 MPa

Yield strength of steel, P(y) = 340 MPa

Factor of safety = 0.3

Allowable stress = 340 * 0.3 = 102 MPa

σ = pr / 2t, where

σ = allowable stress

p = internal pressure

r = radius of the tank

t = minimum wall thickness

t = pr / 2σ

t = 1.5*10^6 * 4.5 / 2 * 102*10^6

t = 0.033 m

t = 33 mm

The minimum thickness of the wall required is therefore, 33 mm

6 0
3 years ago
Other questions:
  • an apple in a tree has a gravitational potential energy of 175J and a mass of 0.36g . how high from the ground is the apple
    14·1 answer
  • Find the work done by the force field F(x, y) = xi + (y + 6)j in moving an object along an arch of the cycloid r(t) = (t − sin(t
    15·1 answer
  • A cart is pulled horizontally with a 156.6 N force to the right at a 67 degree angle with respect to the ground. The cart is mov
    15·1 answer
  • What is the name of the process that describes the decrease in frequency
    7·1 answer
  • A 0.40-μF capacitor is connected to a 5.0-V battery. How much charge is on each plate of the capacitor? Express your answer usin
    15·1 answer
  • A block of mass m1 = 4 kg is moving at 4 m/s and collides with a block of mass m2 = 2 kg, which is moving at 5 m/s in the opposi
    10·1 answer
  • a rock is at the top of a 20 meter tall hill the rock has a mass of 10 kg how much potential does it have
    9·1 answer
  • Which statement about a pair of units is true?
    14·1 answer
  • What mass of water is required to absorb 4.7 x 10 to the 5th power J of energy from a car engine while the temperature increases
    6·1 answer
  • 100 POINTS!!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!