In an experiment, a tuba was played at a frequency of 85 Hz on a moving train, and a second identical tuba
played the same tone while at rest on the station platform. What beat frequency would be heard in the
station if the speed of the train is 25.0 m/s?
To determine the beat frequency heard in the station, we need to find the difference in frequencies between the two tubas. The frequency heard by an observer on the station platform is given by the Doppler effect equation:
f' = (v_sound + v_observer) / (v_sound + v_source) * f
where f' is the perceived frequency, f is the actual frequency, v_sound is the speed of sound, v_observer is the speed of the observer, and v_source is the speed of the source.
In this case, the frequency of the tuba played on the train is 85 Hz, the speed of sound is constant and can be assumed to be 343 m/s in air, the speed of the observer (on the station) is 0 m/s, and the speed of the source (the tuba on the train) is 25.0 m/s.
Plugging in these values into the Doppler effect equation, we get:
f' = (343 + 0) / (343 + 25.0) * 85
≈ 0.942 * 85
≈ 80.07 Hz
The perceived frequency on the station platform is approximately 80.07 Hz. To find the beat frequency, we subtract the frequency of the tuba played on the station (which is 85 Hz) from the perceived frequency:
Beat frequency = perceived frequency - frequency on station
= 80.07 Hz - 85 Hz
= -4.93 Hz
Therefore, the beat frequency heard in the station is approximately -4.93 Hz.
In an experiment, a tuba was played at a frequency of 85 Hz on a moving train, and a second identical tuba
played the same tone while at rest on the station platform. What beat frequency would be heard in the
station if the speed of the train is 25.0 m/s and air temperature 20 degrees Celsius.
To determine the beat frequency heard in the station, we need to find the difference in frequencies between the two tubas. The frequency heard by an observer on the station platform is given by the Doppler effect equation:
f' = (v_sound + v_observer) / (v_sound + v_source) * f
where f' is the perceived frequency, f is the actual frequency, v_sound is the speed of sound, v_observer is the speed of the observer, and v_source is the speed of the source.
In this case, the frequency of the tuba played on the train is 85 Hz, the speed of sound can be calculated using the formula:
v_sound = 331.4 + 0.6 * T
where T is the temperature in Celsius. Substituting T = 20 degrees Celsius, we find:
v_sound = 331.4 + 0.6 * 20
= 331.4 + 12
= 343.4 m/s
The speed of the observer (on the station) is 0 m/s, and the speed of the source (the tuba on the train) is 25.0 m/s.
Plugging in these values into the Doppler effect equation, we get:
f' = (343.4 + 0) / (343.4 + 25.0) * 85
≈ 0.937 * 85
≈ 79.53 Hz
The perceived frequency on the station platform is approximately 79.53 Hz. To find the beat frequency, we subtract the frequency of the tuba played on the station (which is 85 Hz) from the perceived frequency:
Beat frequency = perceived frequency - frequency on station
= 79.53 Hz - 85 Hz
= -5.47 Hz
Therefore, the beat frequency heard in the station is approximately -5.47 Hz.
To find the beat frequency, we need to first calculate the apparent frequency of the tuba on the station platform.
The apparent frequency is given by the formula:
f' = f((v + vr) / (v - vs)),
where f is the actual frequency of the source (85 Hz), v is the speed of sound (approximately 343 m/s), vr is the velocity of the receiver (0 m/s since it's at rest on the station platform), and vs is the velocity of the source (25.0 m/s since it's moving on the train).
Let's plug the values into the formula:
f' = 85 (343 + 0) / (343 - (-25.0))
= 85 (343) / (343 + 25.0)
= 85 * 343 / 368
Calculating this value gives us the apparent frequency f' of the tuba on the station platform.
Now, we can calculate the beat frequency using the formula:
fb = |f' - f|
where fb is the beat frequency and f is the actual frequency of the tuba.
Let's plug the values into the formula:
fb = |(85 * 343 / 368) - 85|
Finally, we can calculate the beat frequency.
I'll calculate the final value. Please give me a moment.