The siren on an ambulance emits a lone described by the following equation where
ID: 1382213 • Letter: T
Question
The siren on an ambulance emits a lone described by the following equation where P is the pressure fluctuation above or below I atm. expressed in pascals (1 Pa = 1 N/m2. x is the distance (in meters), and t is the time in seconds. What is the wavelength (in m) of this sound wave? What is its frequency (in Hi)? What is the speed of these sound waves (in m/s)? What is the pressure (in Pa) at x = 0.500 m at t = 0.0012 s? If you are standing on the sidewalk, what frequency would you hear as this ambulance approaches at a speed of 20 m/s? What frequency would you hear as this ambulance drove away from you at a speed of 20 m/s? Is it a summer or winter day? Explain.Explanation / Answer
compare the given equation with standard equation
p = Pmax*sin(k*x - w*t)
1) so, k = 8*pi/3
2*pi/lamda = 8*pi/3
==> lamda = 6/8
= 0.75 m
2) w = 880*pi
f = w/(2*pi)
= 880*pi/(2*pi)
= 440 Hz
3) v = w/k
= (880*pi)/(8*pi/3)
= 330 m/s
4) at x = 0.5 m, t = 0.0012
p = 1.25*sin(8*pi*0.5/3 - 880*pi*0.0012)
= 0.0136 pa
5) Apply Doppler's effect,
f' = f*v/(v - v_source)
= 440*330/(330 - 20)
= 468.4 Hz
6) Apply Doppler's effect,
f' = f*v/(v + v_source)
= 440*330/(330 + 20)
= 414.86 Hz
It must be a winter day beacuse velocity of sound at T degrees centigrade, v = 331.4 + 0.6*T
330 = 331.4 +0.6*T
T = -2 degrees centigrade( Approximately)
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