a)What frequency is received by a person watching an oncoming ambulance moving at 120 km/h and emitting a steady 700 Hz sound from its siren? The speed of sound on this day is 345 m/s.
b)What frequency does she receive after the ambulance has passed?
Vo=120km/h = 120,000m/3600s = 33.33 m/s.
a. Fr = ((Vs+Vr)/(Vs-Vo))*Fo
Fr=(345+0)/(345-33.33)*700Hz = 774.9 Hz
b. Fr = ((345-0)/(345+33.33))*700=356 Hz
= Freq. heard by the receiver(person).
CORRECTION:
b. Fr = 638.33 Hz.
To calculate the frequency received by a person watching an oncoming ambulance, we can use the formula for the Doppler effect:
f' = f * (v + v₀) / (v + vs)
Where:
f' is the frequency received
f is the source frequency (700 Hz)
v is the speed of sound (345 m/s)
v₀ is the velocity of the observer (in this case, 0 m/s, since the person is stationary)
vs is the velocity of the source (in this case, 120 km/h)
Step 1: Convert the velocity of the source from km/h to m/s:
120 km/h * (1000 m/km) / (60 s/min * 60 min/h) = 33.33 m/s
a) What frequency is received by a person watching an oncoming ambulance?
Using the formula:
f' = 700 Hz * (345 m/s + 0 m/s) / (345 m/s + 33.33 m/s) = 700 Hz * 1 / (1 + 33.33 / 345) ≈ 715.74 Hz
Therefore, the frequency received by the person is approximately 715.74 Hz.
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To calculate the frequency received after the ambulance has passed, we can use the same formula as before:
f' = f * (v - v₀) / (v - vs)
Where:
f' is the frequency received
f is the source frequency (700 Hz)
v is the speed of sound (345 m/s)
v₀ is the velocity of the observer (0 m/s)
vs is the velocity of the source (33.33 m/s)
b) What frequency does she receive after the ambulance has passed?
f' = 700 Hz * (345 m/s - 0 m/s) / (345 m/s - 33.33 m/s) = 700 Hz * 1 / (1 - 33.33 / 345) ≈ 685.33 Hz
Therefore, the frequency received after the ambulance has passed is approximately 685.33 Hz.
To solve this problem, we need to use the concept of Doppler effect. Doppler effect occurs when there is a relative motion between a source of sound and an observer. It causes a change in the perceived frequency of the sound.
a) To find the frequency received by a person watching an oncoming ambulance, we need to consider the motion of the source (ambulance) and the observer (person). The formula to calculate the observed frequency due to the Doppler effect is:
f' = f((v + vr) / (v + vs))
Where:
f' is the observed frequency
f is the emitted frequency by the source
v is the speed of sound
vr is the velocity of the observer relative to the medium (ambulance speed)
vs is the velocity of the source relative to the medium (0 in this case since the observer is stationary)
Given:
Emitted frequency (f) = 700 Hz
Speed of sound (v) = 345 m/s
Ambulance speed (vr) = 120 km/h = 33.33 m/s
Plugging these values into the formula:
f' = 700 * ((345 + 33.33) / (345 + 0))
f' = 700 * (378.33 / 345)
f' = 767.47 Hz (rounded to two decimal places)
Therefore, the frequency received by the person watching the oncoming ambulance is approximately 767.47 Hz.
b) After the ambulance has passed, the relative motion between the source and the observer changes. Now the observer is moving away from the source. The formula for calculating the observed frequency in this case is the same as before:
f' = f((v - vr) / (v + vs))
Using the same values as before, but with the ambulance speed as negative (since it is now moving away):
f' = 700 * ((345 - 33.33) / (345 + 0))
f' = 700 * (311.67 / 345)
f' = 632.82 Hz (rounded to two decimal places)
Therefore, the frequency received by the person after the ambulance has passed is approximately 632.82 Hz.