A violin string vibrates at 196 hz. what frequency will if vibrate with if it is fingered at 1/4 of its length?
Four times as high the original...
Frequency*lambad= vp
216hz
To find the frequency at which the violin string will vibrate when fingered at 1/4 of its length, we can use the equation for the fundamental frequency of a vibrating string. The fundamental frequency is given by the formula:
f = v / (2L)
Where:
- f is the frequency of the vibrating string
- v is the speed of the wave on the string
- L is the length of the vibrating portion of the string
In this case, the original frequency of the violin string is given as 196 Hz. Let's assume that the speed of the wave on the string, v, remains constant.
When the string is fingered at 1/4 of its length, the effective vibrating length of the string becomes 1/4 of the original length. Therefore, we can substitute L/4 for L in the formula:
f' = v / (2 * (L/4))
Simplifying:
f' = v / (2 * L/4)
f' = (v * 4) / (2 * L)
f' = v / L
Since the speed of the wave on the string, v, remains constant, the frequency of the string, f', when fingered at 1/4 of its length is simply the reciprocal of the original length L.
Therefore, the new frequency f' will be four times higher than the original frequency f. In this case, the new frequency f' will be:
f' = 196 Hz * 4
f' = 784 Hz
So, the violin string will vibrate at a frequency of 784 Hz if it is fingered at 1/4 of its length.