A man can hear sounds in frequency range $120\,Hz$ to $12020\,Hz$. only. He is vibrating a piano string having a tension of $240\,N$ and mass of $3\,gm$ . The string has a length of $8\,m$ . How many different frequencies can he hear ?
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$\mathrm{f}=\frac{\mathrm{n}}{2 \mathrm{L}} \sqrt{\frac{\mathrm{T}}{\mu}}$
$\mathrm{f}=\frac{\mathrm{n}}{2 \times 8} \sqrt{\frac{240}{3 \times 10^{-3}} \times 8}=\frac{\mathrm{n} \times 8 \times 10^{2}}{2 \times 8}=50 \mathrm{\,n}$
$\mathrm{n}=3$ to $240 \Rightarrow 238$ frequencies
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