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A $60.0 c m$ guitar string under a tension of $50.0 N$ has a mass per unit length of $0.100 g c m$ What is the highest resonance frequency of the string that can be heard by a person able to hear frequencies upto $20000 H z$ ?

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17 $449 H z$

16 $200 H z$

$19977 H z$

18 $350 H z$

answer is C.

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Detailed Solution

Fundamental frequency.

$f = \frac{v}{2 l} - \frac{\sqrt{T / μ}}{2 l}$

$= \frac{\sqrt{(50) (0.1 \times 10^{- 3} / 10^{- 2})}}{2 \times 0.6}$

$= 58.93 H z$

Let, $n^{t h}$ harmonic is the highest frequency, then

$(58.93) n = 20000$

$n = 339.38$

Hence, $339$ is the highest frequency.

$f_{m a x} = (339) (58.93) H z = 19977 H z$

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