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Llana [10]
3 years ago
9

How long must a flute be in order to have a fundamental frequency of 262 Hz (this frequency corresponds to middle C on the evenl

y tempered chromatic scale) on a day when air temperature is 20.0°C ? It is open at both ends.

Physics
1 answer:
spin [16.1K]3 years ago
7 0

Answer:

L=0.654 m

Explanation:

<u>Concepts and Principles  </u>

1- The speed of sound in air is expressed as a function of the temperature of air as follows:  

 v=(331 m/s)√(1+T_C/273°C)                        (1)

where 331 m/s is the speed of sound in air at temperature 0°C and Tc is the temperature of air in Celsius.  

<u>Standing Wave Patterns in Pipes:  </u>

A pipe open at both ends can have standing wave patterns with resonant frequencies:  

f=v/λ=nv/2L                     n=1,2,3.........

where v is the speed of sound in air.  

<u>Given Data </u>

f_1 (fundamental frequency of the flute) = 262 Hz

T (temperature of the air) = 20°C  

The flute is open at both ends.  

<u>Required Data </u>

We are asked to determine the length of the tube.  

<u>Solution</u><u>  </u>

The speed of sound in air at temperature T = 20°C is found from Equation (1):

 v=(331 m/s)√(1+T_C/273°C)  

 =342.91 m/s

The fundamental frequency of the flute is found by substituting n = 1 into Equation (2):  

f=v/2L

Solve for L:  

L=v/2f_1

L=0.654 m

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Answer:

Explanation:

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A driver travels 135 km, east in 1.5 h, stops for 45 minutes for lunch, and then resumes driving for the next 2.0 h through a di
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<h2>82.353 km/hr</h2>

Explanation:

       The driver travels 135 km towards East in 1.5 hr. He stops for 45 min. He again travels 215 km towards East in 2.0 hr.

       The total displacement of the driver in the given time is ths sum of individual displacements, because all the displacements are in the same directon.

       Total displacement = 135\text{ }km\text{ }East\text{ }+\text{ }0\text{ }km\text{ }+\text{ }215\text{ }km\text{ }East\text{ }=\text{ }350\text{ }km\text{ }East

       Total time travelled = 1.5\text{ }hr\text{ }+\text{ }45\text{ }min\text{ }+\text{ }2.0\text{ }hr\text{ }=\text{ }90\text{ }min\text{ }+\text{ }45\text{ }min\text{ }+\text{ }120\text{ }min\text{ }=\text{ }255\text{ }min\text{ }=\text{ }4\text{ }hr\text{ }15\text{ }min\text{ }=\text{ }4.25\text{ }hr

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Answer:

Option 10. 169.118 J/KgºC

Explanation:

From the question given above, the following data were obtained:

Change in temperature (ΔT) = 20 °C

Heat (Q) absorbed = 1.61 KJ

Mass of metal bar = 476 g

Specific heat capacity (C) of metal bar =?

Next, we shall convert 1.61 KJ to joule (J). This can be obtained as follow:

1 kJ = 1000 J

Therefore,

1.61 KJ = 1.61 KJ × 1000 J / 1 kJ

1.61 KJ = 1610 J

Next, we shall convert 476 g to Kg. This can be obtained as follow:

1000 g = 1 Kg

Therefore,

476 g = 476 g × 1 Kg / 1000 g

476 g = 0.476 Kg

Finally, we shall determine the specific heat capacity of the metal bar. This can be obtained as follow:

Change in temperature (ΔT) = 20 °C

Heat (Q) absorbed = 1610 J

Mass of metal bar = 0.476 Kg

Specific heat capacity (C) of metal bar =?

Q = MCΔT

1610 = 0.476 × C × 20

1610 = 9.52 × C

Divide both side by 9.52

C = 1610 / 9.52

C = 169.118 J/KgºC

Thus, the specific heat capacity of the metal bar is 169.118 J/KgºC

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