What is the Velocity of an Object if Soundwaves Behind it are 3 Octaves Lower?

AI Thread Summary
The discussion revolves around calculating the velocity of an object moving through a medium where sound waves behind it are three octaves lower than those in front. The speed of sound is given as 300 m/s, and it is established that the wavelength behind the object is eight times that in front due to the logarithmic nature of octaves. Participants are seeking equations that relate speed to frequency, specifically referencing the relationship f1 = 8 f2, where f1 is the frequency in front and f2 is behind. There is a suggestion that Doppler effect equations may not be necessary for this problem. The conversation emphasizes the need to clarify the mathematical relationships between frequency and wavelength to solve for the object's velocity.
Anabell
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Homework Statement


Given the speed of sound in an environment, c = 300 m/s. We have an object moving with a ceratin velocity. If we know that the soundwaves behind the object are lower by 3 octaves than in front of it, then what is the velocity of the object?

2. Attempt at solving it.
I arrived at the conclusion that if the wavelength of the soundwaves in front of the object is x, then behind it is eight times of that (eg. x*8), since octaves are on a logaritmic scale. I don't know where to go on from here.
 
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Where are your equations relating speed to frequency.

You know that f1 = 8 f2, where f1 is the frequency in the front and f2 is the frequency behind.

Plug these into your equations relating speed to frequency, and you should be able to solve for the unknown rest frequency and velocity.
(Two equations and two unknowns.)
 
Dr. Courtney said:
Where are your equations relating speed to frequency.

You know that f1 = 8 f2, where f1 is the frequency in the front and f2 is the frequency behind.

Plug these into your equations relating speed to frequency, and you should be able to solve for the unknown rest frequency and velocity.
(Two equations and two unknowns.)
I don't have those equations, could you please ellaborate? :)

Do you mean speed = wavelength * frequency?
 
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You must have Doppler effect equations relating speed and frequency shifts for sources moving toward and away.
 
Anabell said:

Homework Statement


Given the speed of sound in an environment, c = 300 m/s. We have an object moving with a certain velocity. If we know that the soundwaves behind the object are lower by 3 octaves than in front of it, then what is the velocity of the object?

2. Attempt at solving it.
I arrived at the conclusion that if the wavelength of the soundwaves in front of the object is x, then behind it is eight times of that (eg. x*8), since octaves are on a logarithmic scale. I don't know where to go on from here.
I don't think you need to use Doppler effect equations solve this.

If frequency, fB, is one octave above frequency, fA, then how is fB related to fA mathematically?
 

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