If the seventh and fourth standing wave frequencies of a string differ by 144 Hz, what is the fundamental frequency of the string?
the fourth standing wave frequency is 4*f1, where f1 is the fundamental wave frequency. The seventy fundamental frequency is 7*f1
7*f1 - 4*f1 = 3*f1 = 144 hz
f1 = 144/3
This is not correct. The answer is simply as follows:
Let f* be the fundamental frequency.
Then f*[(1/4)-(1/7)]=144Hz.
f* = 1344 Hz
To find the fundamental frequency of the string, we need to determine the frequency difference between consecutive nodal points (or standing waves).
In general, the frequency of a standing wave on a string is given by the formula:
Frequency = n * (v / L)
where n is the harmonic number, v is the velocity of the wave, and L is the length of the string.
In this case, we are given that the seventh (n = 7) and fourth (n = 4) standing wave frequencies differ by 144 Hz. Therefore, we can set up two equations using the formula:
f7 = 7 * (v / L)
f4 = 4 * (v / L)
f7 - f4 = 144 Hz
To find the fundamental frequency, we need to find the difference between the first and second standing waves. Since we have the seventh and fourth frequencies, we need to subtract the fourth frequency from the seventh frequency:
(f7 - f4) = (7 * v / L - 4 * v / L) = (3 * v / L) = 144 Hz
Now we can solve for the fundamental frequency (f1), which is the frequency of the first standing wave (n = 1):
f1 = v / L
To find the numerical value of the fundamental frequency, we need to find the value of v/L. We can do this by dividing both sides of the equation by 3:
v / L = 144 Hz / 3 = 48 Hz
Therefore, the fundamental frequency (f1) of the string is 48 Hz.