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schepotkina [342]
3 years ago
5

Two train whistles have identical frequencies of 180 Hz. When one train is at rest in the station, sounding its whistle, a beat

frequency of 3.7 Hz is heard from a train moving toward us. Find the speed of the train. (Take the speed of sound to be 345 m/s.)
Mathematics
1 answer:
alexgriva [62]3 years ago
5 0

Answer:

7 m/s

Step-by-step explanation:

We are given that

Frequency at stationary =f_0=180Hz

Beat frequency=3.7 Hz

Apparent frequency=f=180+3.7=183.7Hz

Speed of sound=v=345 m/s

We have to find the speed of train

Apparent frequency=f=f_0(\frac{v}{v-v_s})

Substitute the values then we get

183.7=180(\frac{345}{345-v_s})

345-v_s=\frac{180\times 345}{183.7}

345-v_s=338

v_s=345-338=7 m/s

Hence, the speed of train=7 m/s

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The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

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And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be Z_{1-\alpha /2}= Z_{0.975}= 1.96

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n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

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