The fundamental frequency of a plucked wire under a tension of 400N is 250Hz. When the frequency is changed to 500 Hz at constant length, the tension is
-
A.
1600N -
B.
400N -
C.
160N -
D.
40N
Correct Answer: Option A
Explanation
The fundamental frequency is related to tension as
F ∝ √T
| => | F | = K |
| √T |
| ∴ | F1 | = | F2 | => | 250 | = | 500 | √T1 | √T2 | √400 | √T2 |
| ∴√T2 = | 500 | √400 = 2 x 20 |
| 250 |
∴ T2 = 402 = 1600N