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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 A (55.0 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. d det = inches Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.06245 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 A 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 A (55.0 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. d det = inches Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.06245 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 A note? Tafter Tbefore

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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 A (55.0 Hz). If you were to maintain the same tension in the string as with the E string, what diameter ?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.

What is ?det??
 
Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.06245 in. If the tension on your existing string is denoted ?before, by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired A note?
What is ? after/? before??
**Guitar String Detuning Example** 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 A (55.0 Hz). If you were to maintain the same tension in the string as with the E string, what diameter \(d_{det}\) of string would you need to purchase to produce the desired note? Assume all strings available to you are made of the same material. \[ d_{det} = \] ________ inches Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.06245 in. If the tension on your existing string is denoted \(T_{before}\), by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired A note? \[ \frac{T_{after}}{T_{before}} = \] ________ This example involves adjusting guitar string properties—specifically diameter and tension—to change the pitch of the note produced. It easily demonstrates the physics of sound production on string instruments by manipulating physical properties according to target frequencies.
Transcribed Image Text:**Guitar String Detuning Example** 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 A (55.0 Hz). If you were to maintain the same tension in the string as with the E string, what diameter \(d_{det}\) of string would you need to purchase to produce the desired note? Assume all strings available to you are made of the same material. \[ d_{det} = \] ________ inches Unfortunately, none of the strings in your collection have such a large diameter. In fact, the largest diameter you possess is 0.06245 in. If the tension on your existing string is denoted \(T_{before}\), by what fraction will you need to detune (that is, lower the tension) of this string to achieve the desired A note? \[ \frac{T_{after}}{T_{before}} = \] ________ This example involves adjusting guitar string properties—specifically diameter and tension—to change the pitch of the note produced. It easily demonstrates the physics of sound production on string instruments by manipulating physical properties according to target frequencies.
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