A 70.0 c m wire of mass 8.20 g is tied at both ends and adjusted to a tension of

Question

A 70.0cm wire of mass 8.20g is tied at both ends and adjusted to a tension of 41.0N .

A. When it is vibrating in its second overtone, find the frequency at which it is vibrating.

B. When it is vibrating in its second overtone, find the wavelength at which it is vibrating.

C. When it is vibrating in its second overtone, find the frequency of the sound waves it is producing.

D. When it is vibrating in its second overtone, find the wavelength of the sound waves it is producing

Thank you in advance!

Explanation / Answer

(A)
Frequency :
f = c / lambda
= sqrt(T/(m/L)) / lambda
= sqrt(T/(m*L))
= sqrt(41/(0.70 * 0.00820) Hz
= 84.52 Hz

(B)
For the second overtone
wavelength :
lambda = 2 * L/2
       = 2 * 0.70/2
       = 0.70 m

(C)
The frequency will be same .
So f = 84.52 Hz

(D)
Wavelength :
lambda = c/f
       = (343 m/s) /84.52 Hz
       = 4.06 m

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