Musicians can use beats to tune their instruments. One flute is properly tuned and plays the musical note A at exactly 440Hz. A second player sounds the same note and hears that her flute is slightly "flat" (that is, at too low of a frequency). Playing at the same time as the first flute, she hears one loud-soft-loud beat per second.
What is the frequency of her instrument?
I have no clue how to do this, my final is tomorrow. Please help!
To find the frequency of the second player's instrument, we need to understand the concept of beats.
When two sound waves with slightly different frequencies are played together, they interfere with each other, creating a pattern of alternating loud and soft sounds. This pattern is known as beats. The number of beats per second is equal to the difference in frequencies between the two sound waves.
In this case, the second player's flute is slightly "flat," meaning its frequency is lower than the properly tuned flute. Let's assume the frequency of the second flute is f.
We are given that the first flute is tuned to the musical note A, which has a frequency of 440Hz. Since the second flute is slightly flat, its frequency is less than 440Hz.
Now, let's look at the beats. We are told that the second player hears one loud-soft-loud beat per second while playing along with the first flute.
Since the beat frequency is the difference between the two flute frequencies, we can set up the following equation:
|f - 440Hz| = 1 beat/second
The absolute value |f - 440Hz| is used because the beat pattern will still occur whether the second flute is slightly above or below 440Hz.
Now, we can solve the equation to find the frequency of the second flute.
Case 1: f - 440Hz = 1 beat/second
In this case, the frequency of the second flute would be slightly larger than 440Hz.
Case 2: 440Hz - f = 1 beat/second
In this case, the frequency of the second flute would be slightly smaller than 440Hz.
To know which case is correct, we need more information about whether the second flute is slightly higher or lower in frequency compared to the first flute.
In this case, the question does not provide this specific information. So, we cannot determine the exact frequency of the second flute without additional details.
To determine the frequency of the second flute, we need to start by finding the beat frequency between the two flutes.
We are given that the beat frequency is one loud-soft-loud beat per second. This means that the sound waves from the two flutes are interfering constructively and destructively, creating beats.
One beat is produced when the two frequencies differ by one cycle per second. Since the second flute is flat, its frequency is lower than the desired frequency of 440Hz. Let's call the frequency of the second flute f.
We can express the beat frequency (B) as the difference between the two flute frequencies:
B = f - 440Hz
Since we know that there is one beat per second, we can write:
1 beat/second = f - 440Hz
Now we can solve for f:
f = 1 beat/second + 440Hz
Therefore, the frequency of the second flute is 1 beat/second + 440Hz.
it is one hz off, low. 439hz.
I have never heard of a person who can detect lower than 20 hz. In fact, most physics books actually say the range of hearing starts at 20hz.