You are riding your bicycle directly away from a stationary source of sound and hear a frequency that is 2.5% lower than the emitted frequency. The speed of sound at the temperature that day is 339 m/s. What is your speed?
f = f0(v + vo)/v.
Here, vo is the unknown. f = fo*.985
V is 339
1+vo/339 = .985
vo/330=-.025
solve for vo. the negative sign means moving away.
To find your speed, we can use the formula:
f = f0(v + vo)/v
Where:
f = frequency observed
f0 = emitted frequency
v = speed of sound
vo = your speed
In this scenario, we know that the observed frequency (f) is 2.5% lower than the emitted frequency (f0).
So, we have:
f = f0 - 0.025f0
f = 0.975f0
Substituting the values of f and v into the formula, we get:
0.975f0 = f0(v + vo)/v
Now, we can simplify the equation:
0.975v = v + vo
0.975v - v = vo
0.025v = vo
Therefore, we have found that vo (your speed) is equal to 0.025 times the speed of sound (v).
Given that the speed of sound (v) is 339 m/s, we can calculate your speed (vo):
vo = 0.025 x 339
vo = 8.475 m/s
So, your speed is 8.475 m/s, moving away from the stationary source of sound.