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frequency physics question?
A stretched wire vibrates in its first normal mode at a frequency of 352Hz. What would be the fundamental frequency if the wire were half as long, its diameter were doubled, and its tension were increased five-fold?
1 Answer
- billrussell42Lv 73 years agoFavorite Answer
string vibration
v = √(T/μ)
f = (1/(2L))√(T/μ)
v is velocity of propogation
T is tension in string
μ is linear density of the string (mass per unit length)
f is frequency of sound
L is length of string
f = (1/(2L))√(T/μ)
length = 1/2, since they are inversely proportional, f would double
diameter = doubled, then cros-sectional area would go up by a factor of 4, and then linear density would go up by a factor of 4. from the equation, f would go down by 1/√4 = 1/2
tension x5, square root relationship, so f would increase by √5
overall, increase by 2(1/2)√5 = √5 = 2.236
