College

The fundamental frequency of a bass violin string is 1045 Hz and occurs when the string is 0.9 m long. How fast is the string vibrating?

Answer :

The speed of the vibrating bass violin string is 1881 m/s, using the fundamental frequency formula for a string fixed at both ends and given values.

To find the speed at which the string is vibrating, we can use the formula for the fundamental frequency of a string fixed at both ends:

f1 = v / 2L

Where:

f1 is the fundamental frequency (1045 Hz)

v is the wave speed

L is the length of the string (0.9 m)

Rearranging the equation to solve for the wave speed v:

v = 2L * f1

Substitute the given values into the formula:

v = 2 * 0.9 m * 1045 Hz

Calculating the value:

v = 1881 m/s

Thus, the speed at which the string is vibrating is 1881 m/s.