A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a
1.0-m-long rope and whirling it around her head in a horizontal circle at 100 rpm. What are the
highest and lowest frequencies heard by a student in the classroom? (Hint. Find the speed of
the sound generator first)
We will glady critique your work, but you have never shown any here.
7.8hz
To find the highest and lowest frequencies heard by a student in the classroom, we need to calculate the speed of the sound generator first.
First, let's convert the 100 rpm rotation speed to radians per second. Since 1 revolution is equal to 2π radians, we can calculate:
Rotation speed in radians per second = (100 rpm) * (2π radians/1 revolution) * (1 minute/60 seconds)
Now let's calculate the speed of the sound generator. The speed of the sound generator is equal to the tangential velocity of the rope, which is given by:
Tangential velocity = (angular speed) * (radius)
Given that the rope is 1.0 m long, the radius is 1.0 m. We already calculated the angular speed in radians per second, so we can use that value.
Speed of the sound generator = (Rotation speed in radians per second) * (radius)
Now that we have the speed of the sound generator, we can use it to calculate the highest and lowest frequencies heard by a student using the Doppler effect equation:
Frequency = (speed of sound + speed of observer) / (speed of sound)
In this case, the observer is the student in the classroom, and the speed of sound is approximately 343 m/s.
To find the highest frequency, we assume that the sound generator is approaching the student, so the speed of the observer is the speed of sound plus the speed of the sound generator.
To find the lowest frequency, we assume that the sound generator is receding from the student, so the speed of the observer is the speed of sound minus the speed of the sound generator.
Highest frequency = (343 m/s + Speed of the sound generator) / (343 m/s)
Lowest frequency = (343 m/s - Speed of the sound generator) / (343 m/s)
To get the final answer, you can substitute the calculated value of the speed of the sound generator into these equations and calculate the highest and lowest frequencies.