# Doppler effect question

this is from my physics assignment... after pulling half of my hair, i still couldn't figure it out...
my answer for part a) is greater and lower
and part b) is same and same...

not sure tho...
thx

4. Part a) A sister has a ball which she throws toward her brother. The ball is thrown with a velocity, v. The brother stands stationary and catches the ball. Now, if instead the brother is running toward his sister when he catches the ball, would he measure a greater or a lower velocity for the incoming ball (relative to himself)? What about if he is moving away from her when he catches the ball? Remember, velocity is relative. ( /1)

4. Part b) The brother is located some distance from his sister. Both are stationary. She shouts at him with a pure tone (say, 400 Hz). He measures that the velocity of sound (emitted from his sister) is 343 m/s when they are both stationary. They try this experiment a second time, but this time the sister runs toward her brother (he is still stationary). He perceives a higher frequency due to the Doppler effect. If he measures the speed of the sound, would he get the same velocity, higher, or lower than when she was stationary? Finally, what if the brother runs toward his sister, who is stationary. As before, she shouts at 400 Hz, and as before, he perceives a higher frequency. When he measures the speed of the sound from his reference frame, what does he get this time, higher, lower, or the same as when they were both stationary? ( /4) (Explain your answers. be careful – this question is tricky) ( /4)

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HallsofIvy
Homework Helper
a) should be easy- in fact the speeds add so running toward his sister the ball will have a greater speed (relative to the boy) and running away from his sister it will have lower speed (again, relative to the boy) as you say.

b) "Frequency" means how many cycles of the sound wave pass you in a second. That will depend on both how long the wave is and how fast it is moving (think of it like a long train passing while you sit in your car at the crossing).
If each wave has length l meters and is moving at v meters per second, then it will pass in l/v seconds or (inverting) you will see v/l cycles each second: frequency, f= v/l.

We are told that the sister shouts in a "pure tone" at 400 Hz (very impressive, by the way!) and the speed of sound is 343 m/s. Okay "f= v/l" gives 400= 343/l or l= 343/400= 0.8575 meters wavelength.

(I just noticed that the question doesn't ask for specific values so that calculation wasn't really necessary!)

If he measures the speed of the sound, would he get the same velocity, higher, or lower than when she was stationary?
The simple answer to this is that the speed of sound is the speed of the sound in the air- the speed relative to the air is constant. As long as the boy is stationary, relative to the air, it doesn't matter that the girl is running- the speed of the sound is the same. He perceives the sound wave as being "scrunched up"- with shorter wavelength- and so higher frequency.

Finally, what if the brother runs toward his sister, who is stationary.
The sound wave still has the same speed realtive to the air is still 343 m/s but now the boy is moving relative to the air. He would perceive the sound as having a higher speed relative to himself. He would now see the wavelength as being the same as when both were stationary but, since the speed of sound is higher relative to him, the frequency is higher.