An old mining tunnel disappears into a hillside. You would like to know how long the tunnel is, but it's too dangerous to go inside. Recalling your recent physics class, you decide to try setting up standing-wave resonances inside the tunnel. Using your subsonic amplifier and loudspeaker, you find resonances at 5.0 Hz and 6.4 Hz , and at no frequencies between these. It's rather chilly inside the tunnel, so you estimate the sound speed to be 333 m/s .

Answers

Answer 1

Answer:

 L = 116.6 m

Explanation:

For this exercise we approximate the tunnel as a tube with one end open and the other closed, at the open end there is a belly and at the closed end a node, therefore the resonances occur at

               λ = 4L         1st harmonic

               λ = 4L / 3    third harmonic

               λ = 4L / 5    fifth harmonic

General term

               λ = 4L / n      n = 1, 3, 5,...    odd

                                    n = (2n + 1)      n are all integers

They indicate that two consecutive resonant frequencies were found, the speed of the wave is related to the wavelength and its frequency

            v = λ f

            λ = v / f

we substitute

            [tex]\frac{v}{f} = \frac{4L}{n}[/tex]

             L = [tex]n \frac{ v}{4f}[/tex]

for the first resonance n = n

             L = (2n + 1) [tex]\frac{v}{4f_1}[/tex]

for the second resonance n = n + 1

             L = (2n + 3) [tex]\frac{v}{4f_2}[/tex]

we have two equations with two unknowns, let's solve by equating

             (2n + 1) \frac{v}{4f_1}= (2n + 3) \frac{v}{4f_2}

             (2n + 1) f₂ = (2n +3) f₁

              2n + 1 = (2n + 3) [tex]\frac{f_1}{f_2}[/tex]

              2n (1 - \frac{f_1}{f_2}) = 3 \frac{f_1}{f_2} -1

we substitute the values

              2n (1- [tex]\frac{5}{6.4}[/tex]) = 3 [tex]\frac{5}{6.4}[/tex] -1

              2n 0.21875 = 1.34375

              n = 1.34375 / 2 0.21875

              n = 3

remember that n must be an integer.

We use one of the equations to find the length of the Tunal

                  L = (2n + 1) \frac{v}{4f_1}

                  L = (2 3 + 1) [tex]\frac{333}{4 \ 5.0}[/tex]

                  L = 116.55 m


Related Questions

d. Two point charges, q1 = +25 nC and q2 = -75 nC, are separated by a distance of 3.0 cm. Find the magnitude and direction of; i. the electric force q1 exerts on q2 [5] ii. the force that q2 exerts on q1 [4] (take k = 9.0 x 109 N.m2 /C2 )

Answers

Answer:

a) F₂₁ = 0.02 N, attracting.

b) F₁₂ = 0.02 N, attracting.

Explanation:

a)

The magnitude of the force that q₁ exerts on q₂ (F₂₁) is given by Coulomb's Law, as follows:

      [tex]F_{21} = k * \frac{q_{1} *q_{2}}{r_{12}^{2} } = 9e9 N.m2/C2 * \frac{(25e-9C)*(75e-9C)}{(0.03m)^{2}} = 0.02 N (1)[/tex]

Since q₁ and q₂ have opposite signs, the force between them will be always attractive, i.e., from q₂ towards q₁, along the line that joins both charges.

b)

The magnitude of the force on q₁ due to q₂ can be obtained applying Newton's 3rd Law, or using (1), because all parameters are the same, so F₁₂ (in  magnitude) = F₂₁ = 0.02 NAs we have already said, it must be opposite to the one found in a) so it must go from q₁ towards q₂, it is an attracting force also.

5
Select the correct answer.
What is the current in a parallel circuit which has two resistors (17.2 ohms and
22.4 ohms) and a power source of 6.0 volts?
ОА.
0.30 amps
OB.
9.8 amps
OC.
0.61 amps
D.
1.2 amps
Reset
Next

Answers

Answer:

Current in a parallel circuit = 0.61 amps (Approx)

Explanation:

Given:

Voltage V = 6 volt

Two resistors = 17.2 , 22.4 in parallel circuit

Find:

Current in a parallel circuit

Computation:

1/R = 1/r1 + 1 / r2

1/R = 1/17.2 + 1 / 22.4

R = 9.73 ohms (Approx)

Current in a parallel circuit = V / R

Current in a parallel circuit = 6 / 9.73

Current in a parallel circuit = 0.61 amps (Approx)

Four bicyclists travel different distances and times along a straight path. Which cyclist traveled with the greatest average

speed?

A

B

Cyclist 2 travels

87 min 22 s

Cyclist 4 travels

108 min 24 s

D

Cyclist 1 travels

95 m in 27 s

Cyclist 3 travels

106 m in 26 s

Answers

Answer:

The cyclist with the greatest average speed is Cyclist 4 with average speed of 4.5 m/s

Explanation:

Given;

Cyclist 1 travels 9 m    in    27 s

Cyclist 2 travels 87 m  in    22 s

Cyclist 3 travels 106 m  in   26 s

Cyclist 4 travels 108 m   in   24 s

Determine the average speed of the cyclists as follows;

Average speed of Cyclist 1:    v =  9/27  = 0.33 m/s

Average speed of Cyclist 2:    v = 87/22 = 3.96 m/s

Average speed of Cyclist 3:    v =   106/26 = 4.08 m/s

Average speed of Cyclist 4:     v =   108/24 = 4.5 m/s

Therefore, the cyclist with the greatest average speed is Cyclist 4 with average speed of 4.5 m/s

Fifty grams of ice at 0◦ C is placed in a thermos bottle containing one hundred grams of water
at 6◦ C. How many grams of ice will melt? The heat of fusion of water is 333 kJ/kg and the
specific heat is 4190 J/kg · K.Immersive Reader

Answers

Answer:

7.55 g

Explanation:

Given that:

Heat of fusion = 333kj/kg

Heat capacity, c = 4190 j/kg /k

The Number of grams of ice that will melt can be represented as y:

Number of grams of ice that will melt * heat of fusion = specific heat capacity * temperature change

y * 333 * 10^3 J = (4190) * (6 - 0)

333000y = 25140

y = 25140 / 333000

y = 0.0754954 kg

y = 0.0754954 * 100

y = 7.549 g

Hence, Number of grams of ice that will melt = 7.55 g

Which type of biological molecule would contain fats?
A) Amino Acids.
C) Nucleic Acids.
B) Lipids.
D) Carbohydrates.

Answers

B

Explanation:

lipids contains fat

hope it helps

Suppose you are standing at the earth's geographic north magnetic pole, the place on the earth's surface that compasses point toward. You have a compass that is free to swivel in any direction. Which way does your compass point? Suppose you are standing at the earth's geographic north magnetic pole, the place on the earth's surface that compasses point toward. You have a compass that is free to swivel in any direction. Which way does your compass point? It would point up. It would point east. It would point down. It would point west.

Answers

Answer:

It would point up.

Explanation:

Since I am at the earth's geographic north magnetic pole, the place on the earth's surface that compasses point toward, the north pole of the compass would also point towards the earth's geographic north magnetic pole, since all other compasses point toward there.

Since the compass is free to swivel in any direction, the compass would point up, since it is at the earth's geographic north magnetic pole, the place on the earth's surface that compasses point toward.

So, the compass would point up.

12. An organ pipe that is 1.75 m long and open at both ends produces sound of

frequency 303 Hz when resonating in its second overtone. What is the speed of

sound in the room?

295 m/s

328 m/s

354 m/s

389 m/s

401 m/s

Answers

Answer:

354 m/s

Explanation:

For the second overtune (Third harmonic) of an open pipe,

λ = 2L/3................................ Equation 1

Where L = Length of the open pipe, λ = Wave length.

Given: L = 1.75 m.

Substitute into equation 1

λ = 2(1.75)/3

λ = 1.17 m.

From the question,

V = λf.......................... Equation 2

V = speed of sound in the room, f = frequency

Given: f = 303 Hz.

Substitute into equation 2

V = 1.17(303)

V = 353.5

V ≈ 354 m/s

Hence the right answer is 354 m/s

tank contains 335 kg of water at a uniform temperature of 60oC. The tank is insulated and not heated; it neither loses nor gains heat through the walls of the tank. A valve is opened and water exits the tank at a rate of 0.5 kg/sec and a temperature of 60oC. After 10 seconds the valve is closed again . Using the assumption that water at zero degrees centigrade contains zero energy and considering only internal, how much energy left the tank through the valve during this 10 second period; report as kJ.

Answers

Answer:

Explanation:

Thermal energy or internal energy gain or loss = mass x specific heat x temperature  

specific heat of water = 4.2 kJ / kg degree Celsius

mass of water lost in 10 second = rate of loss x time = .5 x 10 = 5 kg .

heat energy associated with lost water = 5 x 4.2 x ( 60 - 0 ) = 1260 kJ .

Heat energy lost = 1260 kJ .

What is a overly-simplified definition of Einstein's theory of general relativity?​

Answers

Answer:

the laws of physics are the same for all non-accelerating observers

Explanation:

a toy of mass 600 is whirled by a child in a horizontal circle using a string of length 2m with a linear speed of 5 m/s determine the angular velocity of the toy?​

Answers

Explanation:

angular velocity = velocity/radius

= 5/2

= 2.5 rad/s

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