The frequency of a stationary siren is 1500 Hz when measured by a stationary observer. If an observer moves away from the siren at mach number .85 what is the frequency he hears? (assume room temperature so that velocity of the air is 340m/s)
I know that I would use f'=f (v - v_o)/(v + v_s)
But what I don't get is the mach number .85
Isn't mach number .85 = v_s/v?
How would I set up this problem?
Should it look like this:
=(1500Hz) (1-0)/(340m/s+.85)
=4.4Hz
Is this correct?
I'm not familiar with that particular term, but mach number .85 could possibly mean 0.85 times the speed of sound.
f'=f(v-vo)/v+vs
To solve this problem, you are correct that you need to use the formula:
f' = f (v - v_o)/(v + v_s)
where f is the frequency observed by the stationary observer, f' is the frequency observed by the moving observer, v is the velocity of sound in air (given as 340 m/s), v_o is the velocity of the observer, and v_s is the velocity of the source (siren).
The Mach number, denoted as M, is defined as the ratio of the velocity of an object to the velocity of sound in the medium. In this case, the Mach number is given as 0.85. Therefore, you can set up the equation:
0.85 = v_o / v
Now, solving for v_o:
v_o = 0.85v = 0.85 * 340 m/s = 289 m/s
Using this value of v_o, you can substitute it into the formula:
f' = f (v - v_o) / (v + v_s)
Substituting the given values:
f' = 1500 Hz * (340 m/s - 289 m/s) / (340 m/s + v_s)
Since the observer is moving away from the siren, the velocity of the source (v_s) will be negative. So, let's assume that v_s = -v_o:
f' = 1500 Hz * (340 m/s - 289 m/s) / (340 m/s - 289 m/s)
f' = 1500 Hz * 51 m/s / 51 m/s
f' = 1500 Hz
Thus, the frequency observed by the moving observer is still 1500 Hz.