Kim is tuning a piano. She strikes a 440 Hz tuning fork and a string at the same time and hears 4 beats per second.
a) What are the possibe frequencies of the string?
b)She tightens the string a little then repeats. She now hears 1 beat per second. What is the frequency of the string?
444, 436 will give a beat of 4
She tightens it, so F goes up. so it must be 439 , and she started low at 436
but I do wonder how she heard 4 beats/sec, then 1beat/second. That is well below the lowest frequency humans can perceive.
To find the possible frequencies of the string, we need to understand the concept of beats in relation to frequencies. When two waves with slightly different frequencies interfere, they create an oscillating sound known as beats. The frequency of the beats tells us how much the two frequencies differ.
a) In this case, Kim strikes a 440 Hz tuning fork, and when it interacts with the string, she hears 4 beats per second. To determine the possible frequencies of the string, we need to calculate the difference between the tuning fork frequency and the string's frequencies that produce the observed beats.
The formula to calculate the difference in frequency is:
Difference in frequency = Number of beats / Time
In our case, the difference in frequency is: 4 beats per second.
Now, we can calculate the possible frequencies of the string:
Possible Frequencies of the string = Tuning fork frequency ± Difference in frequency
For example:
Possible Frequency 1 = 440 Hz - 4 Hz = 436 Hz
Possible Frequency 2 = 440 Hz + 4 Hz = 444 Hz
Therefore, the possible frequencies of the string are between 436 Hz and 444 Hz.
b) Kim tightens the string a little, and now she hears 1 beat per second. To find the frequency of the string, we follow the same steps as before.
Difference in frequency = 1 beat per second
Possible Frequency = Tuning fork frequency ± Difference in frequency
For example:
Possible Frequency 1 = 440 Hz - 1 Hz = 439 Hz
Possible Frequency 2 = 440 Hz + 1 Hz = 441 Hz
Therefore, the frequency of the string, after tightening, is between 439 Hz and 441 Hz.