Problem 12.82: Musical scale. The frequency ratio of a semitone interval on the
ID: 1468590 • 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.
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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
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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.
SubmitMy AnswersGive Up
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.
Equitempered Semitone is 21/12 = 1.059.
Look at 12 semitones i.e. ( 21/12 *21/12* ...........21/12 ) (Total twelve times) = 212/12 =2
This Factor of 2 is what we need to go up by an octave.... Hence Proved...
B.
While approaching
n’ /n = C/(C-V)
or
While receding
n”/n = (C-V)/C
In either case, the ratio of large frequency /smaller frequency =1.059
C/(C-V) = 1.059
C = (C-V)* 1.059
1.059 V = 0.059*330
V = 18.39 m/s