Problem 12.82: Musical scale. The frequency ratio of a semitone interval on the
ID: 1470130 • Letter: P
Question
Problem 12.82: Musical scale.
The frequency ratio of a semitone interval on the equally tempered scale is 21/12.
Part A
Show that this ratio is 1.059.
12rad2
SubmitMy AnswersGive Up
Incorrect; Try Again; 4 attempts remaining
Part B
Find the speed of an automobile passing a listener at rest in still air if the pitch of the car's horn drops a semitone between the times when the car is coming directly toward him and when it is moving directly away from him.
18.94
SubmitMy AnswersGive Up
Incorrect; Try Again; 2 attempts remaining
Problem 12.82: Musical scale.
The frequency ratio of a semitone interval on the equally tempered scale is 21/12.
Part A
Show that this ratio is 1.059.
12rad2
SubmitMy AnswersGive Up
Incorrect; Try Again; 4 attempts remaining
Part B
Find the speed of an automobile passing a listener at rest in still air if the pitch of the car's horn drops a semitone between the times when the car is coming directly toward him and when it is moving directly away from him.
v =18.94
m/sSubmitMy AnswersGive Up
Incorrect; Try Again; 2 attempts remaining
Explanation / Answer
(a)
2^(1/12) = 12 rad 2 = 1.059
Answer for this is 12 rad 2.
(b)
Using Doppler Effect -
[(V+VL)/(V-VS)] / [(V+VL)/(V+VS)] = 2^(1/12)
As the Listener is at Rest
VL = 0
V = 344 m/s
Substituing Values -
(344/344 - VS) / (344/ 344+VS) = 2^(1/12)
344+VS / 344 - VS = 2^(1/12)
VS = 9.93 m/s