A siren on a station platform emits sound that has a frequency of 290 Hz. A passenger on atrain moving away from the station at a constant speed hears a sound of frequency 275 Hzfrom the siren. Calculate the speed of the train
Question
A siren on a station platform emits sound that has a frequency of 290 Hz. A passenger on atrain moving away from the station at a constant speed hears a sound of frequency 275 Hzfrom the siren. Calculate the speed of the train
Solution
To solve this problem, we need to use the formula for the Doppler effect for sound. The formula is:
f' = f * (v + vo) / (v + vs)
where:
- f' is the observed frequency (275 Hz),
- f is the source frequency (290 Hz),
- v is the speed of sound in air (343 m/s),
- vo is the speed of the observer (which is 0 because the observer is stationary),
- vs is the speed of the source (which is the speed of the train we're trying to find).
We can rearrange the formula to solve for vs:
vs = ((f / f') * (v + vo)) - v
Substituting the given values:
vs = ((290 Hz / 275 Hz) * (343 m/s + 0)) - 343 m/s
vs = 17.96 m/s
So, the speed of the train is approximately 17.96 m/s.
Similar Questions
An ambulance is generating a siren sound at a frequency of 2,400 Hz. The speed of sound is 345.0 m/s. If the observer is traveling at a velocity of 24.00 m/s away from the stationary ambulance, then what is the frequency of the siren perceived by the observer?
An ambhulance blowing a siren of frequency 700Hz is travelling slowly towards vertical reflectoing wall with a speed 2m/s. The speed of sound is 350m/s. How many beats ar heard per sec to the driver of het ambluance?
A siren, mounted on a tower, emits a sound whose frequency is 2140 Hz. A car isbeing driven away from the tower at a speed of 25.5 m s‒1, and, as the figureillustrates, the siren sound reaches the driver by two paths: sound coming directlyfrom the siren, and sound reaching the car after reflection from the building. Calculatethe frequency that the driver hears from (i) direct sound and (ii) reflected sound
A train is moving past a crossing where cars are waiting for it to pass. While waiting, the driver of the lead car becomes sleepy and rests his head on the steering wheel, unintentionally activating the car's horn. A passenger in the back of the train hears the horn's sound at a frequency of 435 Hz and a passenger in the front hears it at 413 Hz. Find the train's speed and the horn's frequency, assuming the sound travels along the tracks. Take the speed of sound to be 343 m/s.HINT(a)the train's speed (in m/s) m/s(b)the horn's frequency (in Hz) Hz
An ambulance has just passed by your home. You detect that the frequency of thereceding siren is 900.0 Hz. If you know that the frequency of the ambulance’s sirenis 950.0 Hz, how fast is the ambulance moving? The speed of sound in this case is335 m/s.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.