Temperature and Frequency: Calculating Percent Difference for Piano Tuning

In summary, the conversation discusses a problem involving the tuning of a piano at different temperatures. The equation V = 331 + 0.6(T) is used to calculate the speed of sound at different temperatures, and the square root of temperature is used to find the percent difference between two temperatures. However, the correct answer is not obtained, leading to confusion and speculation about potential errors in the problem or solution.
  • #1
Anony-mouse
60
0

Homework Statement


A piano is to be tuned at 20.0°C. However, when the temperature has lowered to 6.32°C, the piano will be off tune. By what percentage will the piano be off key at this low temperature?


Homework Equations


V = Square Root (3RT/M)


The Attempt at a Solution


T must be in Kelvins, so 20--> 293 K and 6.32--> 279.47 K

Because 3R/M is constant for both temperatures, you can ignore that in the equation so it is just the square root of temperature.
V1 = Sqrt (293)
V2 = Sqrt (279.47)

To find the percent difference, I did (1 - V2/V1) = 0.0234. Thus, the percent difference is 2.34%, but that wasn't the right answer.
 
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  • #2
I just tried doing it a different way, but that still didn't give me the right answer.

V = 331 + .6(T)
V1=343 m/s
V2=334.792 m/s

1-v2/v1 = 0.0239 = 2.39%

I am really confused on this problem if anyone knows what I am doing wrong.
 
  • #3
Where did you get the equation from ?
Are you sure T isn't tension?
 
  • #4
I'm no expert, I'm in grade 11 just like you but I'm a little better at this stuff than the rest... I'm not sure if I'm right, but use the V = 331 + .6(T) formula, and divide the first number (original), by the new number? And you might get a percentage?

mgb_phys said:
Where did you get the equation from ?
Are you sure T isn't tension?

T is the temperature, it is also tension in different equations.
The equation that I repeated (v=) is from the Grade 11 textbook... it is a valid formula.
 
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  • #5
I flipped the equation so that it was V1/V2, which gave a percent of 2.45, but that didn't work either. I don't think this question is supposed to be that difficult, so could it just be a problem with the answer, since I'm pretty sure everything I did was right.

Does anyone notice anything wrong though with the work I did earlier?
 
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What is the relationship between temperature and frequency?

The relationship between temperature and frequency is known as the thermal frequency response. As the temperature increases, the frequency of a system also increases. This is due to the fact that at higher temperatures, particles have more energy and are able to vibrate more quickly, resulting in a higher frequency.

How does temperature affect the speed of sound?

Temperature has a direct effect on the speed of sound. As the temperature increases, the speed of sound also increases. This is because at higher temperatures, air molecules have more energy and are able to vibrate more quickly, resulting in a faster propagation of sound waves.

What is the significance of temperature and frequency in electromagnetic radiation?

Temperature and frequency play a crucial role in the behavior of electromagnetic radiation. As the temperature of an object increases, the frequency of the radiation it emits also increases. This is known as Wien's displacement law. Additionally, the frequency of electromagnetic radiation determines its wavelength, which is important for understanding how it interacts with different materials and objects.

How do temperature and frequency affect the behavior of materials?

Temperature and frequency have a significant impact on the behavior of materials. As temperature increases, the molecules in a material have more energy and are able to move more freely, resulting in changes in properties such as density, thermal expansion, and electrical conductivity. Additionally, different materials have different resonance frequencies, meaning they will vibrate at different frequencies in response to external forces.

What is the role of temperature and frequency in chemical reactions?

Temperature and frequency are important factors in chemical reactions. Increasing the temperature of a reaction typically increases the frequency of collisions between molecules, resulting in a faster reaction rate. Additionally, different chemical reactions have different activation energies, which can be affected by the frequency of collisions between reactant molecules.

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