A group of hikers hears an echo 5.00 s after shouting. How far away is the mount

Question

A group of hikers hears an echo 5.00 s after shouting. How far away is the mountain that reflected the sound wave? (Assume the speed of sound is 348.7 m/s.)

One of the loudest sounds in recent history was that made by the explosion of Krakatoa on August 26-27, 1883. According to barometric measurements, the sound had a decibel level of 180 dB at a distance of 161 km. Assuming the intensity falls off as the inverse of the distance squared, what was the decibel level on Rodriguez Island, 4,800 km away?

An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 471 Hz when the train is approaching him and 454 Hz when the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find?
m/s

Explanation / Answer

1) so distance = 2 L

time = 2L/v

L = v t/2 = 5*348.7/2=871.75 m

2) so 180 = 10 log(I/I0)

I = 10^18*10^-12 = 10^6 = P/(4*pi*161.0E3^2)

P=3.26E17

so at rodriguez I = 3.26E17/(4*pi*4800E3^2)=1126

so dB = 10 log(1126/10^(-12))= 150.5 dB

3) so when coming towards him f = v/(v - vt) f0

when going away f = v/(v + vt) f0

so divide equations

471/454 = (343+v)/(343-v)

v=6.3 m/s

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