Ask question

Ask question

All categories

3 years ago

9

A flute is designed so that it plays a frequency of 261.6 Hz, middle C, when all the holes are covered and the temperature is 20

.0°C. (a) Consider the flute to be a pipe open at both ends and find its length, assuming the middle-C frequency is the fundamental frequency. (Give your answer to at least three decimal places.)(b) A second player, nearby in a colder roomalso attempts to play middle C on an identical flute. A beatfrequency of 3.00 beats/s is heard. What is the temperatureof the room?

1 answer:

irinina [24]3 years ago

4 0

Answer:

0.655 m

13.468°C

Explanation:

v = Speed of sound at 20.0°C = 343 m/s (general value)

For one both end open we have the expression

$L=\dfrac{\lambda_1}{2}\\\Rightarrow L=\dfrac{\dfrac{v}{f_1}}{2}\\\Rightarrow L=\dfrac{\dfrac{343}{261.6}}{2}\\\Rightarrow L=0.655581039755\ m$

The length of the flute is 0.655 m

Beat frequency is given by

$\Delta f=f_1-f_2\\\Rightarrow 3=261.6-f_2\\\Rightarrow f_2=261.6-3\\\Rightarrow f_2=258.6\ Hz$

Velocity of the wave is

$v=f_2\lambda_1\\\Rightarrow v=258.6\times \dfrac{343}{261.6}\\\Rightarrow v=339.066513761\ m/s$

The temperature is given by

$T=273(\dfrac{v}{331})^2\\\Rightarrow T=273(\dfrac{339.066513761}{331})^2\\\Rightarrow T=286.468227799\ K=286.468227799-273=13.468227799^{\circ}C$

The temperature of the room is 13.468°C

You might be interested in

A mass MM uniform solid cylinder of radius RR and a mass MM thin uniform spherical shell of radius RR roll without slipping. If

vampirchik [111]

Answer:

vcyl / vsph = 1.05

Explanation:

The kinetic energy of a rolling object can be expressed as the sum of a translational kinetic energy plus a rotational kinetic energy.
The traslational part can be written as follows:

$K_{trans} = \frac{1}{2}* M* v_{cm} ^{2} (1)$

The rotational part can be expressed as follows:

$K_{rot} = \frac{1}{2}* I* \omega ^{2} (2)$

where I = moment of Inertia regarding the axis of rotation.
ω = angular speed of the rotating object.
If the object has a radius R, and it rolls without slipping, there is a fixed relationship between the linear and angular speed, as follows:

$v = \omega * R (3)$

For a solid cylinder, I = M*R²/2 (4)
Replacing (3) and (4) in (2), we get:

$K_{rot} = \frac{1}{2}* \frac{1}{2} M*R^{2} * \frac{v_{cmc} ^{2}}{R^{2}} = \frac{1}{4}* M* v_{cmc}^{2} (5)$

Adding (5) and (1), we get the total kinetic energy for the solid cylinder, as follows:

$K_{cyl} = \frac{1}{2}* M* v_{cmc} ^{2} +\frac{1}{4}* M* v_{cmc}^{2} = \frac{3}{4}* M* v_{cmc} ^{2} (6)$

Repeating the same steps for the spherical shell:

$I_{sph} = \frac{2}{3} * M* R^{2} (7)$

$K_{rot} = \frac{1}{2}* \frac{2}{3} M*R^{2} * \frac{v_{cms} ^{2}}{R^{2}} = \frac{1}{3}* M* v_{cms}^{2} (8)$

$K_{sph} = \frac{1}{2}* M* v_{cms} ^{2} +\frac{1}{3}* M* v_{cms}^{2} = \frac{5}{6}* M* v_{cms} ^{2} (9)$

Since we know that both masses are equal each other, we can simplify (6) and (9), cancelling both masses out.
And since we also know that both objects have the same kinetic energy, this means that (6) are (9) are equal each other.
Rearranging, and taking square roots on both sides, we get:

$\frac{v_{cmc}}{v_{cms}} =\sqrt{\frac{10}{9} } = 1.05 (10)$

This means that the solid cylinder is 5% faster than the spherical shell, which is due to the larger moment of inertia for the shell.

3 0

3 years ago

Perform the following mathematical operation and report answer to the correct number of significant figures 143.6 divided by 21.

Svetllana [295]

The answer to the correct number of significant figures is 6.774.

<h3>What is quotient?</h3>

When a number(big) divided smaller number, the answer obtained greater than zero is called a quotient.

Divide 143.6 ÷ 21.2

143.6/21.2 = 1436/212

=6.77358

The quotient is rounded to three significant figures after decimal

143.6 ÷ 21.2 = 6.774

Thus, the answer to the correct number of significant figures is 6.774

Learn more about quotient

brainly.com/question/27796160

#SPJ1

7 0

2 years ago

What are some ways you can vary your tone of voice to help you communicate effectively with others? A. Speaking aggressively

Leno4ka [110]

The answer is D, talking more loudly or quietly.
<span>
An expressive voice can bring totally different meaning to what you are saying. If you speak in a monotone voice, you are implying that you do not care about what you are saying or what the other person is talking about. If you speak expressively with some parts quieter or louder to make a point, it lets the listener know that you care about what you are saying and you care about what they have to say too. You can also emphasize a point by speaking louder or indicate that something is not as important by speaking softer.</span>

7 0

3 years ago

Read 2 more answers

Match the following vocabulary words. Match the items in the left column to the items in the right column. 1. the degree of exac

svetlana [45]

1. Avogadro's hypothesis. Avogadro hypothesized that equal volumes of all gases (at the same pressure) will have the same number of molecules. From PV=nRT, we know that one mole of gas takes up 22.4 L
2. Mass number. The mass number is the sum of the protons and neutrons in the nucleus so Carbon 12 has an atomic number of 6 which indicates 6 protons, and a mass number of 12 so 12-6 = 6 neutrons.
3. Avogadro's number. Avogadro's number is the number of units in one mole of any substance, which has been defined as 6.02 x10^23
4. Isotopes are the different forms of a single element. They differ in neutrons. One example is Hydrogen which has three isotopes Protium, Deuterium, and Tritium.
5. Atomic mass. The mass of the atom is equal to the sum of the protons and the neutrons as electrons are so small their mass is negligible. This is not exactly the same as the mass number because this number takes into account the different isotopes
6. mole A mole has the same number of entities as 12 grams of carbon 12, it is expressed by Avogadro's number so 1 mole = 6.02 x10^23 atoms or molecules, etc
7. molar mass- the amount that one mole of substance weighs. For carbon 12, 12 grams has one mole of atoms by definition. So for carbon 12, the molar mass is 12 g/mol

6 0

3 years ago

Read 2 more answers

A long uniformly charged thread (linear charge density λ= 2.5 C/m) lies along the x axis in the figure.(Figure 1) A small charge

Kamila [148]

Answer 1) The electric field at distance r from the thread is radial and has magnitude

E = λ / (2 π ε° r)

The electric field from the point charge usually is observed to follow coulomb's law:

E = Q / (4 π ε° $r^{2}$ )

Now, adding the two field vectors:

$E_{thread}$ = {2.5 / (22 π ε° X 0.07 ) ; 0}

Answer 2) $E_{q}$ = {2.3 / (4 2 π ε°) ( - 7/ (√(84); -12 / (√84))

Adding these two vectors will give the length which is magnitude of the combined field.

The y-component / x-component gives the tangent of the angle with the positive x-axes.

Please refer the graph and the attachment for better understanding.

5 0

3 years ago