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A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 48.0 m/s. What are

astra-53 [7]

Answer: a) 16Hz, 3m b) 48Hz, 1mc) 80Hz, 0.6m

Explanation:

a) Fundamental frequency in string is represented as Fo = V/2L where;

Fo is the fundamental frequency

V is the speed of the transverse wave = 48m/s

L is the length of the wire. = 1.50m

Substituting this values in the formula given we have;

Fo = 48/2(1.5)

Fo = 48/3

Fo = 16Hz

The fundamental tone is therefore 16Hz

Using v =f¶

Where f is the frequency and ¶ is the wavelength, the wavelength of the fundamental note will be;

¶ = v/fo

¶ = 48/16 = 3m

b) Overtones or harmonics is the multiple integral of the fundamental frequency. The multiples are I'm arithmetical progression.

First overtone f1 = 2fo

Second overtone f2 = 3fo etc.

Since fo = 16Hz

Second overtone f2 = 3×16 = 48Hz

¶ = v/f2 = 48/48

¶ = 1m

c) Fourth harmonic or overtone will be f4 = 5fo

F4 = 5×16 = 80Hz

The fourth harmonic is therefore 80Hz

¶ = v/f4 = 48/80

¶ = 0.6m

4 0

3 years ago

STATE THE LAWS OF CONSERVATION OF MOMENTUM

dalvyx [7]

$\Huge \mid \underline {\mathcal {{{\color{purple}{Answer...}}}}} \mid$

When two bodies collide with each other in the absence of an external force, then the total final momentum of the bodies is equal to their total initial momentum.

6 0

3 years ago

The plates of a parallel-plate capacitor are 2.50 mm apart, and each carries a charge of magnitude 80.0 nC. The plates are in va

bonufazy [111]

Answer:

10000 V

0.00225988700565 m²

$8\times 10^{-12}\ F$

Explanation:

E = Electric field = $4\times 10^6\ V/m$

d = Gap = 2.5 mm

Q = Charge = 80 nC

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

Potential difference is given by

$V=Ed\\\Rightarrow V=4\times 10^6\times 2.5\times 10^{-3}\\\Rightarrow V=10000\ V$

The potential difference between the plates is 10000 V

Area is given by

$A=\dfrac{Q}{\epsilon_0E}\\\Rightarrow A=\dfrac{80\times 10^{-9}}{8.85\times 10^{-12}\times 4\times 10^6}\\\Rightarrow A=0.00225988700565\ m^2$

The area of the plate is 0.00225988700565 m²

Capacitance is given by

$C=\dfrac{\epsilon_0A}{d}\\\Rightarrow C=\dfrac{8.85\times 10^{-12}\times 0.00225988700565}{2.5\times 10^{-3}}\\\Rightarrow C=8\times 10^{-12}\ F$

The capacitance is $8\times 10^{-12}\ F$

4 0

3 years ago

A thin, rectangular sheet of metal has mass M and sides of length a and b. Find the moment of inertia of this sheet about an axi

Lubov Fominskaja [6]

Answer:

The moment of inertia is $I=\frac{M}{12} a^{2}$

Explanation:

The moment of inertia is equal:

$I=\int\limits^a_b {r^{2} } \, dm$

If r is $-\frac{a}{2}$

and $dm=\frac{M}{a} dr$

$I=\int\limits^a_b {r^{2}\frac{M}{a} } \, dr\\a=\frac{a}{2} \\b=-\frac{a}{2}$

$I=\frac{M}{a} \int\limits^a_b {r^{2} } \, dr\\\\I=\frac{M}{a} (\frac{M}{3} )_{b}^{a}\\ I=\frac{M}{3a} (\frac{a^{3} }{8} +\frac{a^{3} }{8} )\\I=\frac{M}{12} a^{2}$

7 0

3 years ago

Two stars orbit each other in a _ solar system

Brilliant_brown [7]

This is a binary star system

4 0

4 years ago

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