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Andreas93 [3]
3 years ago
13

Find the three longest wavelengths (call them λ1, λ2, and λ3) that "fit" on the string, that is, those that satisfy the boundary

conditions at x=0 and x=l. these longest wavelengths have the lowest frequencies. express the three wavelengths in terms of l. list them in decreasing order of length, separated by commas.

Physics
1 answer:
zepelin [54]3 years ago
6 0
If you have a string that is fixed on both ends the amplitude of the oscillation must be zero at the beginning and the end of the string. Take a look at the pictures I have attached. It is clear that  our fundamental harmonic will have the wavelength of:
\lambda_1=\frac{L}{2}
All the higher harmonics are just multiples of the fundamental:
\lambda_n=n\lambda_1\\ \lambda_n=n\frac{L}{2}
Three longest wavelengths are:
n=3; \lambda_3=\frac{3L}{2}\\
n=2; \lambda_2=L\\
n=1; \lambda_=\frac{L}{2}\\


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Two boats leave the same port at the same time, with boat A traveling north at 15 knots (nautical miles per hour) and boat B tra
Mrrafil [7]

Answer:

The chance in distance is 25 knots

Explanation:

The distance between the two particles is given by:

s^2 = (x_A - x_B)^2+(y_A - y_B)^2  (1)

Since A is traveling north and B is traveling east we can say that their displacement vector are perpendicular and therefore (1) transformed as:

s^2 = x_B^2+y_A^2 (2)

Taking the differential with respect to time:

\displaystyle{2s\frac{ds}{dt}= 2x_B\frac{dx_B}{dt}+2y_A\frac{dy_A}{dt}}  (3)

where \displaystyle{\frac{dx_B}{dt}}=v_B and \displaystyle{\frac{dx_A}{dt}}=v_A are the respective given velocities of the boats. To find s and x_B we make use of the given position for A, y_A=30, the Pythagoras theorem and the relation between distance and velocity for a movement with constant velocity.

\displaystyle{y_A = v_A\cdot t\rightarrow t = \frac{y_A}{v_A}=\frac{30}{15}=2 h

with this time, we know can now calculate the distance at which B is:

\displaystyle{x_B = v_B\cdot t= 20 \cdot 2 = 40\ nmi

and applying Pythagoras:

\displaystyle{s = \sqrt{x_B^2+y_A^2}=\sqrt{30^2 + 40^2}=\sqrt{2500}=50}

Now substituting all the values in (3) and solving for  \displaystyle{\frac{ds}{dt} } we get:

\displaystyle{\frac{ds}{dt} = \frac{1}{2s}(2x_B\frac{dx_B}{dt}+2y_A\frac{dy_A}{dt})}\\\displaystyle{\frac{ds}{dt} = 25 \ knots}

4 0
3 years ago
What is the best unit to use when measuring the mass of a mineral sample?
Ksivusya [100]
Measuring density: Measure the mass (in grams) of each mineral sample available to you. The mass of each sample is measured using a balance or electronic scale. Record mass on a chart.
8 0
2 years ago
A light ray incident on a block of glass makes an incident angle of 50.0° with the normal to the surface. The refracted ray in t
Vladimir [108]

Answer:

The index of refraction of the glass is 1.3

Explanation:

Given data:

i = incident angle = 50°

r = refracted angle = 36.1°

The index of refraction according Snell´s law is:

n=\frac{1*sini}{sinr} =\frac{1*sin50}{sin36.1} =1.3

4 0
3 years ago
A block of 250-mm length and 54 × 40-mm cross section is to support a centric compressive load P. The material to be used is a b
musickatia [10]

Answer:

P = 17.28*10⁶ N

Explanation:

Given

L = 250 mm = 0.25 m

a = 0.54 m

b = 0.40 m

E = 95 GPa = 95*10⁹ Pa

σmax = 80 MPa = 80*10⁶ Pa

ΔL = 0.12%*L = 0.0012*0.25 m = 3*10⁻⁴ m

We get A as follows:

A = a*b = (0.54 m)*(0.40 m) = 0.216 m²

then, we apply the formula

ΔL = P*L/(A*E)  ⇒ P = ΔL*A*E/L

⇒  P = (3*10⁻⁴ m)*(0.216 m²)*(95*10⁹ Pa)/(0.25 m)

⇒  P = 24624000  N = 24.624*10⁶ N

Now we can use the equation

σ = P/A

⇒  σ = (24624000  N)/(0.216 m²) = 114000000 Pa = 114 MPa > 80 MPa

So σ > σmax  we use σmax

⇒  P = σmax*A = (80*10⁶ Pa)*(0.216 m²) = 17280000 N = 17.28*10⁶ N

7 0
2 years ago
True Or False? The tendency for an object in motion to remain in motion is called orbital speed.
Harlamova29_29 [7]

The correct answer to the question is False i.e the tendency of an object in motion to remain in motion is not called the orbital speed.

EXPLANATION:

Before going to answer this question, first we have to understand Newton's first laws of motion.

As per Newton's first laws of motion, every body continues to be in state of rest or of uniform motion in a straight line unless and until it is compelled by some external unbalanced forces.

Hence, as long as no unbalanced force is acting on a moving object, it will be in motion. This tendency of a moving object to be in motion is called inertia of motion of the body.

Inertia of motion is the property of the body by virtue of which a moving body always tries to be in motion.

Hence, the tendency of an object in motion to remain in motion is not called as the orbital speed.

7 0
3 years ago
Read 2 more answers
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