Calculating Frequency Shift for Temperature Change in Musical Instruments

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In summary, the first question asks how far from the end of an unfingered guitar string must the finger be placed to play a certain note. Using the equation v=(frequency)(wavelength), the distance was found to be 0.525 m. The second question involves finding the change in frequency of an organ at different temperatures. Using the equation v=\sqrt{\frac{\gamma RT}{M}}, it was determined that the speed of sound varies with the square root of temperature.
  • #1
Gauss177
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Homework Statement


1. An unfingered guitar string is 0.70 m long and is tuned to play E above middle C (330 Hz). How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?

2. An organ is in tune at 20 degrees C. By what fraction will the frequency be off at 0 degrees C?

Homework Equations



The Attempt at a Solution



1. I used the v=(freq)(wavelength) equation:
v = (330)(0.70) = 231 m/s
Then i plugged in 231 to figure out the distance for 440 Hz:
(231 m/s) = (440)x
x=.525 m
I'm not sure if my method is right, so please check that! thanks

2. Not sure about this one

Thanks for the help
 
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  • #2
I think that's right.

For the second part,
[tex]v=\sqrt{\frac{\gamma RT}{M}}[/tex] The temperature should be in Kelvin. Since there is no change in the gas, [tex]\frac{\gamma R}{M}[/tex] are constant, and so the speed of sound varies with the square root of temperature. That should help you out.
 
  • #3
!



Your method for calculating the distance for 440 Hz on the guitar string is correct. In order to play A above middle C, the finger must be placed 0.525 m from the end of the string. This is because frequency and wavelength are inversely proportional, meaning as frequency increases, wavelength decreases. Therefore, in order to increase the frequency from 330 Hz to 440 Hz, the wavelength must be shortened by 1/3, resulting in the finger being placed 1/3 of the original distance from the end of the string.

For the second question, we can use the equation f = f0(1+αΔT), where f is the new frequency, f0 is the original frequency, α is the temperature coefficient of the material (which varies for different materials), and ΔT is the change in temperature. In this case, we are looking for the fraction by which the frequency will change, so we can rearrange the equation to solve for the fraction:
f/f0 = 1+αΔT
We know that at 20 degrees C, the frequency is in tune, so f = f0. Plugging this into the equation, we get:
f0/f0 = 1+αΔT
1 = 1+αΔT
Therefore, the frequency will not change at all when the temperature decreases from 20 degrees C to 0 degrees C. This is because the temperature coefficient for most materials used in musical instruments is very small, so the change in frequency is negligible.
 

What is frequency shift for temperature change?

Frequency shift for temperature change refers to the change in pitch or frequency of a musical instrument in response to a change in temperature. As temperature affects the materials and dimensions of the instrument, it can alter the way sound waves travel through it, resulting in a change in frequency.

How does temperature affect the frequency of a musical instrument?

Temperature can affect the frequency of a musical instrument in two main ways. First, the material of the instrument can expand or contract with changes in temperature, which can alter the dimensions of the instrument and thus the frequency of the sound it produces. Second, temperature can affect the speed of sound waves, which can also impact the frequency of the instrument.

What is the formula for calculating frequency shift for temperature change?

The formula for calculating frequency shift for temperature change is Δf = (α x L x ΔT) / 2, where Δf is the change in frequency, α is the coefficient of thermal expansion for the material of the instrument, L is the length of the instrument, and ΔT is the change in temperature.

How accurate is the frequency shift calculation for temperature change?

The accuracy of the frequency shift calculation for temperature change depends on various factors, such as the precision of the instrument's dimensions and the accuracy of the coefficient of thermal expansion used in the calculation. In general, it provides a good estimate of the frequency change, but it may not account for all factors that can affect the instrument's frequency.

Can frequency shift for temperature change be compensated for in musical instruments?

Yes, frequency shift for temperature change can be compensated for in musical instruments. This can be achieved by making adjustments to the instrument's dimensions or materials, or by using electronic tuning devices. Additionally, some musicians may make manual adjustments while playing to compensate for any changes in frequency due to temperature.

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