Rank the beat frequency from highest to lowest for the following pairs of sounds:a. 876 Hz, 871 Hz b. 786 Hz, 784 Hz c. 721 Hz, 728 Hz d. 542 Hz, 541 Hz
f = f(1) -f(2).
f1 =876 - 541 =335 Hz.
f2 =876 -542 =334 Hz...and so on
To rank the beat frequency from highest to lowest for the given pairs of sounds, we need to calculate the absolute difference between the frequencies in each pair. The beat frequency is equal to the absolute difference.
a. 876 Hz, 871 Hz:
Beat frequency = |876 Hz - 871 Hz| = 5 Hz
b. 786 Hz, 784 Hz:
Beat frequency = |786 Hz - 784 Hz| = 2 Hz
c. 721 Hz, 728 Hz:
Beat frequency = |721 Hz - 728 Hz| = 7 Hz
d. 542 Hz, 541 Hz:
Beat frequency = |542 Hz - 541 Hz| = 1 Hz
From highest to lowest beat frequency:
c. 721 Hz, 728 Hz (7 Hz)
a. 876 Hz, 871 Hz (5 Hz)
b. 786 Hz, 784 Hz (2 Hz)
d. 542 Hz, 541 Hz (1 Hz)
To determine the beat frequency for each pair of sounds, we need to find the difference between the frequencies of the two sounds. The beat frequency is the absolute value of this difference.
a. For the pair 876 Hz and 871 Hz, the difference in frequency is 876 Hz - 871 Hz = 5 Hz. Therefore, the beat frequency is 5 Hz.
b. For the pair 786 Hz and 784 Hz, the difference in frequency is 786 Hz - 784 Hz = 2 Hz. Therefore, the beat frequency is 2 Hz.
c. For the pair 721 Hz and 728 Hz, the difference in frequency is 728 Hz - 721 Hz = 7 Hz. Therefore, the beat frequency is 7 Hz.
d. For the pair 542 Hz and 541 Hz, the difference in frequency is 542 Hz - 541 Hz = 1 Hz. Therefore, the beat frequency is 1 Hz.
Now, let's rank the beat frequencies from highest to lowest:
c. 721 Hz, 728 Hz -> Beat Frequency: 7 Hz
a. 876 Hz, 871 Hz -> Beat Frequency: 5 Hz
b. 786 Hz, 784 Hz -> Beat Frequency: 2 Hz
d. 542 Hz, 541 Hz -> Beat Frequency: 1 Hz
Therefore, the beat frequencies ranked from highest to lowest are:
1. 7 Hz
2. 5 Hz
3. 2 Hz
4. 1 Hz