Doppler effect ball throw question

[andytran]

i'm reposting this here because for some reason my post moved to grade k-12 forum... btw this is a first year University physics 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)

 

[lavalamp]

You have the first three answers correct so I will only talk about the last question.
When he runs towards his sister, although the speed of sound moves towards the boy at 343m/s, he is running towards the sound at, say, 5 m/s. This means that relative to the boy the sound is traveling at 348 m/s. Therefore it would take a shorter time for the sound to reach him. The doppler effect doesn't affect the speed of sound, just the frequency.

 

[andytran]

thanks!

and thank god i found this forum hehehe!

 

[andytran]

ahh my teacher throw another similar question... exact wording as the above, but this time is light instead of sound wave. doppler effect behave similarly in all waves right? so the answer would be the same as the sound example.?

thx

 

[lavalamp]

All the answers will not be the same at all.
Relative to any observer, the speed of light is always the same. This is because if you speed up, time for you slows down (relative to the space around you). So when you see a beam of light go past you, you see it go past at the speed of light relative to you.

So if the boy runs towards his sister, the speed of light is good old c, although the light would be "blue shifted" (frequency moved towards the blue end of the spectrum) and if he was running away from his sister the light would be "red shifted" (frequency moved towards the red end of the spectrum). Colour shifts are the electro-magnetic wave equivalent of the doppler effect so these answers would be the same as the answers for sound, however the speed that he measures for the value of c would be constant (2.997 * 10⁸ m/s in a vacuum).