Question

Two instruments having stretched strings are being played in unison. When the tension of one of the instruments is increased by 1%, 3 beats are produced in 2sec, the initial frequency of vibration of each wire is:

• A. 300 Hz
• B. 500 Hz
• C. 1000 Hz
• D. 400 Hz

Answer 1

The correct option is A

300 Hz

$f=\frac{1}{2\pi }\sqrt{\frac{T}{u}}f\propto \sqrt{T}\frac{f-f}{f}\times 100=K\frac{\sqrt{T-T}}{\sqrt{T}}\times 100\frac{3}{2f_0}=\frac{1}{2}\times 1\%\frac{3}{2f_0}=\frac{1}{2}\times \frac{1}{100}{f}_0=300Hz$