Question

The first overtone of a stretched wire of given length is $320 \,Hz$. The first harmonic is :

• A. 320 Hz
• B. 160 Hz
• C. 480 Hz
• D. 640 Hz

Answer 1

Answer: (B)

160 Hz

Answer 2

If a wire, vibrates in p segments, then its frequency is given by
$n=\frac{p}{2 l} \sqrt{\frac{T}{m}}$
The frequency of first harmonic is
$n=\frac{1}{2 l} \sqrt{\frac{T}{m}}\,\,\, ...(i)$
The frequency of second harmonic or first overtone is
$n'=\frac{2}{2 l} \sqrt{\frac{T}{m}}\,\,\, ...(ii)$
$n'=2 n$
$n=\frac{n'}{2}=\frac{320}{2}=160 \,Hz$