Question

5. Two ships in a heavy fog are blowing their horns of 175 Hz when they approach each other at constant speeds. The slower of the two ships has a
speed of 20.0 m/s. (I) What is the speed of the other ship if an observer on a stationary boat nearby between the two ships hears a beat frequency of
5.5 Hz? (II) While the ships are still approaching each other, the observer begins to move at 10.0 m/s towards one of the ships. The beat frequency
the observer hears has increased by at least 10 Hz. Is the observer moving towards the slower ship or the faster ship? Speed of sound = 343.0m/s

Answer 1

given :

f = frequency emitted by the ships = 175 Hz

the ships are moving towards each other.

v1 = speed of slower ship = 20 m/s

v2 = speed of faster ship = ?

v = speed of sound = 343 m/s

a) beat frequency observed by the stationary observer between them = 5.5 Hz.

frequency observed by the observer due to faster ship is f2.

therefore, Applying Doppler's Effect :

----(i)

frequency observed by observer due to slower ship is f1.

therefore, Applying Doppler's Effect :

-----(ii)

beat frequency = f2 -f1

=> v2 = = 29.28m/s [answer]

b) when the observer moving with a speed 10m/s towards one of the ship, the beat frequency becomes at least15.5 Hz.

Lets assume the observer is moving towards faster ship. [if f2-f1 comes out positive then my assumption is true]

frequency observed by the observer due to faster ship is f2.

therefore, Applying Doppler's Effect :

----(i)

frequency observed by observer due to slower ship is f1.

therefore, Applying Doppler's Effect :

-----(ii)

therefore,

.

my assumption is true, that the the observer is moving towards faster ship. [answer]