Calculating Mass Needed for Piano String Resonance at 260 Hz

In summary: However, without knowing the exact value of n, we cannot say for sure if this is the only possible harmonic to produce resonance.
  • #1
MAins
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Question: On a piano, middle C's 260 Hz. What mass is needed then to suspend from a hanger for resonance at 260 Hz for your string (in the absence of a tuning fork)? Is this sensible?

Given:
mstring = 0.0003 kg
Lstring = 1.809 m (entire length of string)
L = 1.370 m (length between fixed points)

And:
f = (n/2L)*sqrt((mhanger*g)/(mstring/Lstring)

I'm unsure what n to use. In the given experiment we used a tuning fork and changed the mass at the end of the hanger to vary tension and n (harmonic). But how does the absence of a tuning fork affect this? Will there be only one possible harmonic to produce resonance or what?
 
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  • #2
Answer: Without a tuning fork, it is not possible to determine the exact mass needed to suspend from a hanger for resonance at 260 Hz for your string. However, based on the given information, you can make an estimate of the mass. Using the equation provided in the question, we can plug in the values for mstring, Lstring, and L. If we set n = 1 (the fundamental frequency), then we can calculate the mass needed for resonance at 260 Hz. This gives us a value of mhanger = 0.0034 kg. This is the estimated mass needed for resonance in the absence of a tuning fork.
 
  • #3


I would first clarify the parameters of the experiment with the person asking the question. It is not clear what is meant by "suspension from a hanger" and how that would affect the resonance of the piano string. Additionally, the use of a tuning fork and changing the mass at the end of the hanger suggests that the experiment is attempting to determine the relationship between tension and harmonic frequency, rather than calculating the mass needed for resonance at a specific frequency.

Assuming that the experiment is trying to determine the relationship between tension and harmonic frequency, the given formula is correct. However, as the question mentions, the value of "n" is unclear without the use of a tuning fork. In the absence of a tuning fork, there will still be multiple possible harmonics that can produce resonance at 260 Hz. The specific harmonic will depend on the length and tension of the string.

To determine the mass needed for resonance at 260 Hz, the experiment would need to be set up in a way that allows for the manipulation of tension and measurement of the resulting frequency. The mass needed can then be calculated using the given formula, with the appropriate value of "n" determined through experimentation.

Overall, the question is not entirely clear and more information is needed to provide a definitive answer. As a scientist, it is important to clarify experimental parameters and ensure that the question being asked is accurately represented.
 

1. How is the mass needed for piano string resonance calculated?

The mass needed for piano string resonance at a specific frequency, such as 260 Hz, is calculated using the equation: mass = (length of string * frequency^2)/(2 * string tension * square of the string diameter). This equation takes into account the length and tension of the string, as well as the thickness of the string.

2. What is the significance of 260 Hz in piano string resonance?

260 Hz is a commonly used frequency for calculating mass needed for piano string resonance, as it is within the range of frequencies produced by most pianos. It also falls within the range of human hearing, making it a suitable frequency for tuning and testing piano strings.

3. What units are used to measure the mass needed for piano string resonance?

The mass needed for piano string resonance is typically measured in grams (g) or kilograms (kg), depending on the size and thickness of the string. The length of the string is usually measured in meters (m) and the frequency is measured in hertz (Hz).

4. Are there any other factors that can affect the calculation of mass needed for piano string resonance?

Yes, there are a few other factors that can affect the calculation of mass needed for piano string resonance. These include the material and density of the string, as well as any vibrations or interference from other strings or objects. These factors may require adjustments to the equation or the use of a more advanced calculation method.

5. Can the mass needed for piano string resonance be calculated for all types of pianos?

Yes, the mass needed for piano string resonance can be calculated for all types of pianos, as long as the necessary information about the string length, tension, and diameter is available. However, the actual mass needed may vary depending on the quality and condition of the piano, so it is best to consult a professional for an accurate calculation.

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