A violinist tunes her third \"A\" string to exactly 440 Hertz, which matches the

Question

A violinist tunes her third "A" string to exactly 440 Hertz, which matches the piano A_4. The violinist then tunes her next (4th) string E_5 a perfect 5th higher. Since a perfect 5th is in ratio of 3:2 what is the frequency of the E_5 string? The piano however uses equal temperament tuning. The E_5 frequency is 7 semitones higher so the piano E_5 frequency is: f = 440 times (2)^7/12. Try to calculate it. Then compare your result to the table in the back cover of your book. What will be the beat frequency between the violin and piano at the E_5 notes? [Recall that the "beat" frequency between two frequencies is given: f_b = f_2 - f_1] Do you think this beat frequency will be noticeable?

Explanation / Answer

a) E5 has a frequency 1.5 times higher, thus 660Hz

b) Using the given formula one has f=659.255Hz

c) Beat frequency is thus fb=0.745Hz

d) This frequency is not noticeable since the minumum frequency human ear detects is 20Hz.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.