A source of sound emits waves at a frequency f= 650 Hz. An observer is located at a distance d= 170 m from the source. Use u=340 m/s for the speed of sound.
(a) Assume completely still air. How many wavefronts (full waves) N are there between the source and the observer?
N=
unanswered
(b) If the observer is moving away from the source at a (radial) velocity v=40 m/s, how does the number of wavefronts N found in part (a) change with time? For the answer, give the rate of change of N, namely dNdt (in Hz)
dN/dt=
unanswered
(c) By comparing the difference of the rate of wavefronts leaving and wavefronts entering the region between source and observer, calculate the frequency f′ observed by the moving observer. (in Hz)
hint: how does the difference relate to the rate of change of N you calculated in (b)?
f′=
unanswered
(d) Let us now assume that both source and observer are at rest, but wind blows at a constant speed v=20 m/s in the direction source towards observer. By comparing the difference of the rate of wavefronts leaving and wavefronts entering the region between source and observer, calculate the observed frequency f′? (in Hz)
f′=
d : distance
f : freq
v_s: 340m/s
a) N = df/(v_sound) (1)
b) asume that d = vt .
plug into eq(1):
N(t) = vtf/v_s => N(t) = (vf/v_s)t
and so d/dt of that is vf/v_s
prove this to yourself by working out the answer to (a) using this.
c) use ((v_s+v_0)/v_s)*f watch your signs, remember that if the source and observer are moving apart, f should be smaller. so it could be either (v_s+v_0) or (v_s-v_0) in the numerator.
d) f' = f
Anonymous can u explain c onemore time?
are you sure about d???
I thought the wind will increase the frequency of the source
Andy, for C)
f'=f(1- vobs/vsound)
Can some explain Part d of doppler shift. I used the following: f'= f*(1+speed of observer/speed of sound)
f'=450*(1+20/340)=450*1.0588=476.46. This is my last chance. The wind blows toward the observer. Any ideas. Thanks.
it doesnt matter if the wind blows, so its the same frequency. In your case 450.
guys where did you find those equations, lecture num or book chapt pls?
part d- f'=f
explanation: in case of wind blowing, we'll add the speed of wind to the speed of sound (vectorially). Hence in this case it will add up. Now since the both the observer and the source are stationary, there will be no change in the frequency of sound.
NOTE: frequency will change if there is relative motion between the observer and the source.
FORMULA: f'=f((v+wind-u1)/(v+wind-u2))
v-speed of sound
u1-observer speed
u2-source speed
wind-wind speed (add vectorially)
(a) To determine the number of wavefronts (full waves) between the source and the observer, we can use the formula:
N = d / λ
where N is the number of wavefronts, d is the distance between the source and the observer, and λ is the wavelength of the sound wave.
In this case, we are given the distance (d = 170 m) and the frequency (f = 650 Hz) of the sound wave. The speed of sound (u) is also given as 340 m/s.
To find the wavelength, we can use the formula:
λ = u / f
Substituting the given values, we have:
λ = 340 m/s / 650 Hz ≈ 0.523 m
Now, we can find the number of wavefronts:
N = 170 m / 0.523 m ≈ 325.33
Since we are looking for the number of wavefronts (full waves), we can round down to the nearest integer:
N ≈ 325
Therefore, the number of wavefronts (full waves) between the source and the observer is approximately 325.
(b) We are now given that the observer is moving away from the source at a radial velocity of v = 40 m/s. This means that the distance between the source and the observer is increasing.
The rate of change of the number of wavefronts, dN/dt, represents how the number of wavefronts changes with time. In this case, since the distance between the source and the observer is increasing, the number of wavefronts will decrease over time.
To find dN/dt, we can use the formula:
dN/dt = -v / λ
where v is the radial velocity and λ is the wavelength.
Substituting the given values, we have:
dN/dt = -40 m/s / 0.523 m ≈ -76.45 Hz/s
Therefore, the rate of change of the number of wavefronts is approximately -76.45 Hz/s.
(c) The observed frequency, f', by the moving observer can be calculated by considering the difference in the rates of wavefronts leaving and entering the region between the source and the observer.
Since the observer is moving away from the source, the rate at which wavefronts leave the region is decreased by the value of dN/dt (calculated in part b). The observed frequency can be found using the formula:
f' = f - dN/dt
Substituting the given values, we have:
f' = 650 Hz - (-76.45 Hz/s) = 726.45 Hz
Therefore, the observed frequency by the moving observer is approximately 726.45 Hz.
(d) In this case, both the source and the observer are at rest, but there is wind blowing at a constant speed of v = 20 m/s from the source towards the observer.
Similar to the previous case, we consider the difference in the rate of wavefronts leaving and entering the region between the source and the observer.
Since the wind is blowing towards the observer, the rate at which wavefronts enter the region is increased by the value of dN/dt. Therefore, the observed frequency, f', can be calculated using the formula:
f' = f + dN/dt
Substituting the given values, we have:
f' = 650 Hz + (-76.45 Hz/s) = 573.55 Hz
Therefore, the observed frequency in this case is approximately 573.55 Hz.