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3 years ago

12

A speaker is designed for wide dispersion for a high frequency sound. What should the diameter of the circular opening be in a s

peaker where the desired diffraction angle is 75° and a 9100 Hz sound is generated? The speed of sound is 343 m/s

1 answer:

Greeley [361]3 years ago

6 0

Answer:

$a = 4.76 cm$

Explanation:

As we know by the law of diffraction through circular aperture

$a sin\theta = 1.22 \lambda$

here we know that

a = diameter of the aperture

$\theta$ = diffraction angle

$\lambda$ = wavelength

now we have

$a = \frac{1.22 \lambda}{sin\theta}$

Now in order to find the wavelength we know

$\lambda = \frac{c}{f}$

$\lambda = \frac{343}{9100}$

$\lambda = 0.0376 m$

now we have

$a = \frac{1.22(0.0376)}{sin75}$

$a = \frac{0.046}{0.966}$

$a = 0.0476 m= 4.76 cm$

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A solid conducting sphere of radius 2 cm has a charge of 8microCoulomb. A conducting spherical shell of inner radius 4 cm andout

nika2105 [10]

Answer:

C) 7.35*10⁶ N/C radially outward

Explanation:

If we apply the Gauss'law, to a spherical gaussian surface with radius r=7 cm, due to the symmetry, the electric field must be normal to the surface, and equal at all points along it.
So, we can write the following equation:

$E*A = \frac{Q_{enc} }{\epsilon_{0}} (1)$

As the electric field must be zero inside the conducting spherical shell, this means that the charge enclosed by a spherical gaussian surface of a radius between 4 and 5 cm, must be zero too.
So, the +8 μC charge of the solid conducting sphere of radius 2cm, must be compensated by an equal and opposite charge on the inner surface of the conducting shell of total charge -4 μC.
So, on the outer surface of the shell there must be a charge that be the difference between them:

$Q_{enc} = - 4e-6 C - (-8e-6 C) = + 4 e-6 C$

Replacing in (1) A = 4*π*ε₀, and Qenc = +4 μC, we can find the value of E, as follows:

$E = \frac{1}{4*\pi*\epsilon_{0} } *\frac{Q_{enc} }{r^{2} } = \frac{9e9 N*m2/C2*4e-6C}{(0.07m)^{2} } = 7.35e6 N/C$

As the charge that produces this electric field is positive, and the electric field has the same direction as the one taken by a positive test charge under the influence of this field, the direction of the field is radially outward, away from the positive charge.

6 0

3 years ago

A solenoidal coil with 26 turns of wire is wound tightly around another coil with 350 turns. The inner solenoid is 20.0 cm long

noname [10]

Answer:

Part a)

$\phi = 2.76 \times 10^{-7} T m^2$

Part B)

$M = 5.52 \times 10^{-5} H$

Part C)

$EMF = 0.1 V/s$

Explanation:

Part a)

Magnetic field due to a long ideal solenoid is given by

$B = \mu_0 n i$

n = number of turns per unit length

$n = \frac{N}{L}$

$n = \frac{350}{0.20}$

$n = 1750 turn/m$

now we know that magnetic field due to solenoid is

$B = (4\pi \times 10^{-7})(1750)(0.100)$

$B = 2.2 \times 10^{-4} T$

Now magnetic flux due to this magnetic field is given by

$\phi = B.A$

$\phi = (2.2 \times 10^{-4})(\pi r^2)$

$\phi = (2.2 \times 10^{-4})(\pi(0.02)^2)$

$\phi = 2.76 \times 10^{-7} T m^2$

Part B)

Now for mutual inductance we know that

$\phi_{total} = M i$

$\phi_{total} = N\phi$

$\phi_{total} = 20(2.76 \times 10^{-4})$

$\phi_{total} = 5.52 \times 10^{-6}$

now we have

$M = \frac{5.52 \times 10^{-6}}{0.100}$

$M = 5.52 \times 10^{-5} H$

Part C)

As we know that induced EMF is given as

$EMF = M \frac{di}{dt}$

$EMF = 5.52 \times 10^{-5} (1800)$

$EMF = 0.1 V/s$

3 0

4 years ago

A wave with low energy will also have

Aliun [14]

Will also have low frequency

3 0

3 years ago

Ice has a specific heat of 2.093Jg ∘C, liquid water's specific heat is 4.184Jg ∘C, and steam has a specific heat of 1.864Jg ∘C.

Ivan

Answer:

The liquid phase will have the lowest temperature change upon heating.

Explanation:

Assuming no phase change due to heating, we know that the temperature change, is proportional to the mass heated, being the proportionality constant a quantity that depends on the material, and represents the resistance of the material to change the temperature, called specific heat.

So, if we assume that the mass is the same for the three phases, and that the amount of heat supplied is also the same,the phase with the highest specific heat will have the lowest temperature change.

So, the liquid phase will be the one that exhibits this behavior, as the specific heat of liquid water (4.184 J/gºC) is the highest among the three phases.

8 0

3 years ago

in a tall building, a certain window is 500 meters above the ground.A tennis ball is catapulted horizontally out of the window w

expeople1 [14]

The tennis ball lands at a point 40.4 m from the base of the building.

The tennis ball is projected with a horizontal velocity <em>u</em> from a window, which is at a height <em>y</em> from the ground. The ball lands at a distance <em>x</em> from the base of the building. Let the ball take a time <em>t</em> to reach the ground. In the time <em>t</em> ,the ball falls a vertical distance <em>y</em> and also travel a horizontal distance <em>x</em>.

The initial vertical velocity of the ball is zero, since the ball is projected in the horizontal direction. The ball falls down under the action of gravitational force.

Thus, use the equation of motion,

$y=\frac{1}{2} gt^2$

rewrite the expression for <em>t</em> and calculate the value of <em>t</em> using 9.81 m/s²for <em>g</em> and 500 m for <em>y</em>.

$t=\sqrt{\frac{2y}{g} } \\ =\sqrt\frac{(2)(500m)}{9.81m/s^2} \\ =10.096 s$

The horizontal distance <em>x</em> is traveled using the constant velocity <em>u </em>since no force acts on the ball in the horizontal direction.

Therefore,

$x=ut$

Substitute 4 m/s for <em>u</em> and 10.096 s for <em>t</em>

$x=ut\\ =(4m/s)(10.096s)\\ =40.384m=40.4 m$

Thus, the ball lands at a point 40.4 m from the base of the building.

6 0

3 years ago