In one of the original Doppler experiments, one tuba was played on a moving platform car at a frequency of 75 Hz, and a second identical one was played on the same tone while at rest in the railway station. What beat frequency was heard if the train approached the station at a speed of 18.0 m/s?
calculate the doppler frequency , then the difference in that and 75 is the beat.
that answer is not helpful enough to someone who is struggling with the material.
f'=f(v)/(v-vs)=75(340)/(340-18)=DO MATH
fbeat=f'-f
so sub f from calculated #
To determine the beat frequency, we need to calculate the difference in frequency between the two tubas.
The Doppler effect formula can be used to find this. The formula for the apparent frequency when the source is moving towards the observer is:
f' = (v + vo) / (v + vs) * f
where:
f' = apparent frequency
v = speed of sound in air
vo = velocity of observer (positive if moving towards the source)
vs = velocity of source (positive if moving away from the observer)
f = actual frequency
Given:
f = 75 Hz (frequency of tuba at rest in the railway station)
vs = 0 m/s (velocity of source at rest)
v = 343 m/s (speed of sound in air)
We need to find the value of vo.
Using the formula, we can rearrange it to solve for vo:
vo = ((f' * v) + (-vs * f)) / f
Substituting the known values:
vo = ((f' * v) + (0 * 75)) / 75
vo = (f' * v) / 75
Now, we can calculate the apparent frequency, f', using the given information that the train is approaching the station at a speed of 18.0 m/s.
f' = (v + vo) / (v + vs) * f
Substituting the known values:
f' = (343 + vo) / (343 + (-18)) * 75
Simplifying:
f' = (343 + vo) / 325 * 75
Combining the two equations:
vo = (f' * v) / 75
vo = (343 + vo) / 325 * 75
Now, we can solve for vo:
75vo = 343 + vo
74vo = 343
vo = 4.635 m/s
Now, we can calculate the beat frequency. The beat frequency is the absolute value of the difference in frequency between the two tubas.
beat frequency = |f' - f|
Substituting the known values:
beat frequency = |f' - f|
beat frequency = |((343 + vo) / 325 * 75) - 75|
Substituting the value of vo:
beat frequency = |((343 + 4.635) / 325 * 75) - 75|
beat frequency ≈ |75.171 - 75|
Therefore, the beat frequency heard when the train approaches the station at a speed of 18.0 m/s is approximately 0.171 Hz.
To find the beat frequency heard in this situation, we need to understand the concept of the Doppler effect. Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.
In this case, the source of the sound is the tuba being played on the moving platform car, and the observer is stationary at the railway station.
The formula for the Doppler effect with a moving source and stationary observer is given by:
f' = f * (v + V) / (v - V)
Where:
f' is the apparent frequency heard by the observer
f is the actual frequency of the source
v is the speed of sound (which is approximately 343 m/s)
V is the velocity of the source relative to the medium (in this case, the train moving towards the station)
In this scenario, the actual frequency of the tuba being played is 75 Hz, and the train is moving towards the station at a speed of 18.0 m/s. We can now substitute these values into the formula to calculate the apparent frequency heard:
f' = 75 * (343 + 18) / (343 - 18)
f' = 75 * 361 / 325
f' ≈ 82.92 Hz
Therefore, the beat frequency heard is approximately 82.92 Hz.