A drummer begins to drum on iron railway tracks with a regular beat. You are nea

Question

A drummer begins to drum on iron railway tracks with a regular beat. You are nearby with your ear near the tracks and hear two sets of drumming, one starting 0.8 s after the other. (The speed of sound in air is 345 m/s and in iron is 5,000 m/s.)

(a)    How far away are you from the drummer?

(b)    If the delayed sounds are 5 dB less intense than the first set of drumming heard, find the ratio of the intensities of the two sounds.

(c) If the drummer drums at a frequency of 4 Hz, what frequency will a person hear on a train approaching at 60 mph (conversion factor: 1 mph _ 0.45 m/s)?

please show all work. thanks in advance

Explanation / Answer

let the distance is d

time taken by sound to travel in air =d/345

time taken by sound to travel on tracks =d/5000

now given that both sounds reach in a gap of 0.8s

hence d/345-d/5000=0.8

d(931/345000)=0.8= 296.4m

b) let intensity for first sound be I1

intensity in db =10log(I1/I0)

let intensity for second sound be I2

intensity in db =10log(I2/I0)

given that difference in both intensity in db =5

5= 10log(I1/I0)-10log(I2/I0)

0.5 =log(I1/I0)-log(I2/I0)

0.5 =log(I1/I2)

10^0.5=I1/I2

I1/I2 =3.1622

c)

60mph = 60*0.45m/s -27m/s

frequency heard = ((345+27)/345) *4 (f' = ((Vsound+vlistener)/vsound)*f)

=4.313 Hz

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