Speed in air is 340m.s Siren of ambulance emits waves of frequency 980Hz A detector at the scene measures the frequency as 1050Hz h0w d0 I w0rk this 0ut
1050 = 340 / 340 - vs (980)
1050 = 1 - vs (980)
1050 = -vs (980)
1050 + vs = 980
1050/1050 + vs = 980 / 1050
vs = 980 / 1050
Vs = 0.93
Fd = (Vs+Vd)/(Vs-Va)*Fa = 1050 Hz.
(340+0)/(340-Va) * 980 = 1050
Divide both sides by 980:
340/(340-Va) = 1.0714
364.29-1.0714Va = 340
-1.0714Va = 340-364.29 = -24.29
Va = 22.7 m/s. = Velocity of the ambulance.
Vs = Velocity of sound.
Vd = Velocity of the detector.
To work out the solution, you can use the formula for the Doppler effect:
f = (v + vs) / (v - vs) * f0
Where:
f0 is the frequency of the source (980 Hz in this case).
f is the measured frequency (1050 Hz in this case).
v is the speed of sound in air (340 m/s in this case).
vs is the speed of the source relative to the medium (what we want to calculate).
You have plugged in the values correctly, but let's correct the steps:
Step 1: Calculate the numerator: (v + vs):
(v + vs) = 340 + vs
Step 2: Plug in the values into the formula:
(1050 Hz) = ((340 + vs) / (340 - vs)) * (980 Hz)
Step 3: Solve for vs:
(1050 Hz) * (340 - vs) = (340 + v_s) * (980 Hz)
1050 * 340 - 1050 * vs = 340 * 980 + vs * 980
Step 4: Simplify the equation:
357,000 - 1050vs = 333,200 + 980vs
Step 5: Rearrange the equation and solve for vs:
1050vs + 980vs = 357,000 - 333,200
2030vs = 23,800
vs = 23,800 / 2030
vs â 11.72 m/s
Therefore, the speed of the ambulance is approximately 11.72 m/s.