On a guitar, the lowest-toned string is usually strung to the E note, which produces sound at 82.4 Hz. The diameter of E guitar strings is typically 0.0500 in, and the scale length between the bridge and nut (the effective length of the string) is 25.5 in. Various musical acts tune their E strings down to produce a "heavier" sound or to better fit the vocal range of the singer. As a guitarist you want to detune the E on your guitar to C (65.4 Hz). If you were to maintain the same tension in the string as with the E string, what diameter ddet Of string would you need to purchase to produce the desired note? Assume all strings available to you are made of the same material. ddet = inches Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.05650 in. If the tension on your existing string is denoted Tpefore, by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired C note? Tafter Tbefore
On a guitar, the lowest-toned string is usually strung to the E note, which produces sound at 82.4 Hz. The diameter of E guitar strings is typically 0.0500 in, and the scale length between the bridge and nut (the effective length of the string) is 25.5 in. Various musical acts tune their E strings down to produce a "heavier" sound or to better fit the vocal range of the singer. As a guitarist you want to detune the E on your guitar to C (65.4 Hz). If you were to maintain the same tension in the string as with the E string, what diameter ddet Of string would you need to purchase to produce the desired note? Assume all strings available to you are made of the same material. ddet = inches Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.05650 in. If the tension on your existing string is denoted Tpefore, by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired C note? Tafter Tbefore
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![### Understanding String Tension and Frequency on a Guitar
On a guitar, the lowest-toned string is usually strung to the E note, which produces sound at 82.4 Hz. The diameter of E guitar strings is typically 0.0500 inches, and the scale length between the bridge and nut (the effective length of the string) is 25.5 inches.
Various musical acts tune their E strings down to produce a "heavier" sound or to better fit the vocal range of the singer. As a guitarist, you may want to detune the E on your guitar to C (65.4 Hz). If you were to maintain the same tension in the string as with the E string, what diameter \( d_{\text{det}} \) of string would you need to purchase to produce the desired note? Assume all strings available to you are made of the same material.
\[
d_{\text{det}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{inches}
\]
Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.05650 inches. If the tension on your existing string is denoted \( T_{\text{before}} \), by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired C note?
\[
\frac{T_{\text{after}}}{T_{\text{before}}} = \_\_\_\_\_\_\_
\]
### Detailed Explanation of the Problem
- **Given Information:**
- The standard E string has a frequency of 82.4 Hz.
- The standard E string diameter is 0.0500 inches.
- The scale length of the guitar string is 25.5 inches.
- Desired frequency is the C note at 65.4 Hz.
- **Task 1: Calculating the Diameter for Detuning to C (65.4 Hz):**
- You need to determine the new string diameter \( d_{\text{det}} \) to maintain the same tension while changing the frequency from 82.4 Hz (E note) to 65.4 Hz (C note).
- **Task 2: Adjusting Tension with a Maximum Diameter of 0.05650 inches:**
- Given](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02a699f1-d60c-495e-b821-a86bb0a104cb%2Fe1c118c5-1e5e-4866-bf6f-c641bb635b3e%2Fqv1gq2w_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding String Tension and Frequency on a Guitar
On a guitar, the lowest-toned string is usually strung to the E note, which produces sound at 82.4 Hz. The diameter of E guitar strings is typically 0.0500 inches, and the scale length between the bridge and nut (the effective length of the string) is 25.5 inches.
Various musical acts tune their E strings down to produce a "heavier" sound or to better fit the vocal range of the singer. As a guitarist, you may want to detune the E on your guitar to C (65.4 Hz). If you were to maintain the same tension in the string as with the E string, what diameter \( d_{\text{det}} \) of string would you need to purchase to produce the desired note? Assume all strings available to you are made of the same material.
\[
d_{\text{det}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{inches}
\]
Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.05650 inches. If the tension on your existing string is denoted \( T_{\text{before}} \), by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired C note?
\[
\frac{T_{\text{after}}}{T_{\text{before}}} = \_\_\_\_\_\_\_
\]
### Detailed Explanation of the Problem
- **Given Information:**
- The standard E string has a frequency of 82.4 Hz.
- The standard E string diameter is 0.0500 inches.
- The scale length of the guitar string is 25.5 inches.
- Desired frequency is the C note at 65.4 Hz.
- **Task 1: Calculating the Diameter for Detuning to C (65.4 Hz):**
- You need to determine the new string diameter \( d_{\text{det}} \) to maintain the same tension while changing the frequency from 82.4 Hz (E note) to 65.4 Hz (C note).
- **Task 2: Adjusting Tension with a Maximum Diameter of 0.05650 inches:**
- Given
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