Question

Two violinists are playing their "A" strings. Each is perfectly tuned at 440 Hz and under 245 N of tension. If one violinist turns her peg to tighten her A string to 251 N of tension, what beat frequency will result

Answer 1

Answer:

450.78Hz

Explanation:

The frequency of wave in string is directly proportional to its tension. This is mathematically expressed as

F∝T

F = kT where k is the constant of proportionality

From the formula, k = F/T

F1/T1 = F2/T2 = k

If each violin is perfectly tuned at 440 Hz and under 245 N of tension then F1 = 440Hz, T1 = 245N

To get the frequency if the string A is tighten to 251N of tension,

T2 = 251N, F2 =?

Substituting the given values into the equation above to get F2 we have;

440/245 = F2/251

Cross multiplying

245F2 = 440×251

245F2 = 110,440

F2 = 110,440/245

F2 = 450.78Hz