Question

Modern International Maritime Organization (IMO) regulations specify that ships longer than 200 m must have a ship's whistle whose frequency is between 70 and 192 Hz. Suppose that a 235-m ship has a whistle whose frequency is 187 Hz. If the ship is stationary, what is the maximum speed that an approaching observer can have so that the ship's whistle still satisfies IMO regulations?

Two trains are traveling on the same track and in the same direction. The first train is moving at a speed of 37.2 m/s and blows its horn, whose frequency is 255 Hz. The second train, which is behind the first, detects a frequency of 238 Hz. What is the speed of the second train?

Two trains are traveling on the same track and in the same direction. The first train, which is behind the second train, blows a horn whose frequency is 265 Hz. The second train detects a frequency of 284 Hz. If the speed of the second train is 14.0 m/s, what is the speed of the first train?

Answer 1

1)

Frequency of ships horn: f_o = 187 Hz

The speed of sound: V = 340 m/s

Let the speed with which observer moves be v_o

The source is stationary, so according to doppler, the apparent frequency heard by the observer:

So, for maximum speed of observer, the frequency should also be max.

2)

Speed of first train (source) : v_s = 37.2 m/s

Frequency of source: f_o = 255 Hz

Frequency heard by second train: f = 238 Hz

Speed of second train (observer): v_o

So, according to doppler's:

3)

Speed of first train (source) : v_s

Frequency of source: f_o = 265 Hz

Frequency heard by second train: f = 284 Hz

Speed of second train (observer): v_o = 14 m/s

So, according to doppler's:

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