4) Dr. Scott is running north down the hall in the Science building -his speed i

Question

4) Dr. Scott is running north down the hall in the Science building -his speed is 25 m/sec (yes, he is fast!). You are also walking North (further down the hall) - but at a slower speed. Dr. Scott seems to be whistling a perfect 500 Hz tone. Assume the velocity of sound is 340 m/sec. a) You hear a frequency of 507.9365 Hz from Dr. Scott (you have very accurate ears!). Calculate your speed (and direction .. is it also to the North or is it to the South). b) You should find that you are moving away from the source (Dr. Scott)-but, the frequency you heard is higher than 500 hz.. should it be lower? Explain conceptually (no numbers needed). c) Dr. Moschelli steps out into the hall to the South (behind Dr. Scott-he is standing at rest. calculate the frequency that HE hears from Dr. Scott?

Explanation / Answer

Doppler Effect in sound

From the given situation the observer and the source are in motion and the source is approaching the observer

given f = 500 Hz

observed frequency or apparent frequay is f' = 507.9365 Hz , Dr. Scott speed vs = 25 m/s , vo = ?

from Doppler effect , the apparent change in frequency due to relative motion between the source and observer.

the apparent frequency is f' = f (v-v0 /v-vs)

Vs is speed of the source and V0 is speed of observer , v speed of sound in air = 343 m/s

a)

substituting the given values  

f' = f (v-v0 /v-vs)

f' = f (v-v0 /(v-vs))

507.9365 = 500 (343-vo/(343-25))

vo = 19.9524 m/s m/s

you are moving with a speed of 19.9524 m/s down the hall (north direction)

b)

from the doppler effect in sound the frequency heard by the observer who is moving away from the source should observe the lower frequency than the original frequency of the source

if the frequency of the source is 500 Hz , the frequency heard by you must be lower than 500 Hz when you are moving away from the source

c) The freuency heard by Dr. Moschelli who is at rest is

f' = f (v-v0 /v-vs)

f' = f (v/(v+vs))

f' = 500 (343/(343+25)) Hz

f' = 466 Hz

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.