A wire of length one metre under a certain initial tension emits a sound of fundamental frequency 256 Hz. When the tension is increased by 1 kg wt, the frequency of the fundamental node increases to 320 Hz. The initial tension is.

Question

A wire of length one metre under a certain initial tension emits a sound of fundamental frequency 256 Hz. When the tension is increased by 1 kg wt, the frequency of the fundamental node increases to 320 Hz. The initial tension is. (A) 3/4 kg wt (B) 4/3 kg wt (C) 16/9 kg wt (D) 20/9 kg wt

Tardigrade Admin · Accepted Answer

Let tension be T f1=√(T/μ) × (1/2 l)=256 ldots (i) f2=√(T+10/μ) × (1/2 l)=320 ldots (ii) √(T/T+10)=(256/320) [Dividing (i) by (ii)] or (T/T+10)=((16)2/(16)2 ×(20)2) or (T/T+10)=(162/(20)2) or 400 T=256 T2+2560 or 144 T=2560 or T=(2560/144) or T=(2560/16 × 9) or T=(160/9) Newton =(16/9) kg - wt

Q. A wire of length one metre under a certain initial tension emits a sound of fundamental frequency 256Hz. When the tension is increased by 1kgwt, the frequency of the fundamental node increases to 320Hz. The initial tension is.

3/4 kg wt

4/3 kg wt

16/9 kg wt

20/9 kg wt

Let tension be T f1​=μT​​×2l1​=256… (i) f2​=μT+10​​×2l1​=320… (ii) T+10T​​=320256​ [Dividing (i) by (ii)] or T+10T​=(16)2×(20)2(16)2​ or T+10T​=(20)2162​ or 400T=256T2+2560 or 144T=2560 or T=1442560​ or T=16×92560​ or T=9160​ Newton =916​kg−wt

Q. A wire of length one metre under a certain initial tension emits a sound of fundamental frequency $256 Hz$ . When the tension is increased by $1 k g wt$ , the frequency of the fundamental node increases to $320 Hz$ . The initial tension is.