Starting at middle C, with a frequency of 260 cps, find the frequency of the following notes. a. seven half-steps above middle C b. a fifth (seven half-steps) above middle C c. two octaves and a fifth (seven half-steps) above middle C d. 27 half-steps above middle C a. The frequency of seven half-steps above middle C is cps. (Round to the nearest integer as needed.) b. The frequency of a fifth (seven half-steps) above middle C is cps. (Round to the nearest integer as needed.) c. The frequency of two octaves and a fifth (seven half-steps) above middle C is cps. (Round to the nearest integer as needed.) d. The frequency of 27 half-steps above middle C is cps. (Round to the nearest integer as needed.)
Starting at middle C, with a frequency of 260 cps, find the frequency of the following notes. a. seven half-steps above middle C b. a fifth (seven half-steps) above middle C c. two octaves and a fifth (seven half-steps) above middle C d. 27 half-steps above middle C a. The frequency of seven half-steps above middle C is cps. (Round to the nearest integer as needed.) b. The frequency of a fifth (seven half-steps) above middle C is cps. (Round to the nearest integer as needed.) c. The frequency of two octaves and a fifth (seven half-steps) above middle C is cps. (Round to the nearest integer as needed.) d. The frequency of 27 half-steps above middle C is cps. (Round to the nearest integer as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
![### Frequency Calculation from Middle C
**Problem Statement:**
Starting at middle C, with a frequency of 260 cps, find the frequency of the following notes:
a. Seven half-steps above middle C
b. A fifth (seven half-steps) above middle C
c. Two octaves and a fifth (seven half-steps) above middle C
d. 27 half-steps above middle C
---
**Calculations:**
To calculate the frequencies, use the formula for frequency of a note \( n \) half-steps away from a given frequency \( f \):
\[ f_n = f \times 2^{n/12} \]
Where:
- \( f = 260 \) cps (frequency of the middle C)
- \( n \) is the number of half-steps above middle C.
---
**Questions & Steps:**
a. **The frequency of seven half-steps above middle C is** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) **cps.**
\( n = 7 \)
Calculating \( f_7 \):
\[ f_7 = 260 \times 2^{7/12} \]
(Round to the nearest integer as needed.)
b. **The frequency of a fifth (seven half-steps) above middle C is** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) **cps.**
Note: This is the same as question **a** since a fifth above middle C is also seven half-steps.
Calculating \( f_7 \):
\[ f_7 = 260 \times 2^{7/12} \]
(Round to the nearest integer as needed.)
c. **The frequency of two octaves and a fifth (seven half-steps) above middle C is** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) **cps.**
\( n = 31 \) (24 for two octaves and 7 for the fifth)
Calculating \( f_{31} \):
\[ f_{31} = 260 \times 2^{31/12} \]
(Round to the nearest integer as needed.)
d. **The frequency of 27 half-steps above middle C is** \(\_\_\_\_\_\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4f07f1fc-c1c5-43de-ad13-01ae8930f316%2F24ee8826-2738-43be-9882-a1f31633ad3a%2Fmpiig28_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Frequency Calculation from Middle C
**Problem Statement:**
Starting at middle C, with a frequency of 260 cps, find the frequency of the following notes:
a. Seven half-steps above middle C
b. A fifth (seven half-steps) above middle C
c. Two octaves and a fifth (seven half-steps) above middle C
d. 27 half-steps above middle C
---
**Calculations:**
To calculate the frequencies, use the formula for frequency of a note \( n \) half-steps away from a given frequency \( f \):
\[ f_n = f \times 2^{n/12} \]
Where:
- \( f = 260 \) cps (frequency of the middle C)
- \( n \) is the number of half-steps above middle C.
---
**Questions & Steps:**
a. **The frequency of seven half-steps above middle C is** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) **cps.**
\( n = 7 \)
Calculating \( f_7 \):
\[ f_7 = 260 \times 2^{7/12} \]
(Round to the nearest integer as needed.)
b. **The frequency of a fifth (seven half-steps) above middle C is** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) **cps.**
Note: This is the same as question **a** since a fifth above middle C is also seven half-steps.
Calculating \( f_7 \):
\[ f_7 = 260 \times 2^{7/12} \]
(Round to the nearest integer as needed.)
c. **The frequency of two octaves and a fifth (seven half-steps) above middle C is** \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) **cps.**
\( n = 31 \) (24 for two octaves and 7 for the fifth)
Calculating \( f_{31} \):
\[ f_{31} = 260 \times 2^{31/12} \]
(Round to the nearest integer as needed.)
d. **The frequency of 27 half-steps above middle C is** \(\_\_\_\_\_\
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
