First slide

Standing waves

Question

A stretched string of 1 m length, fixed at both ends, having amass of 5 x 10^-4 kg is under tension of 20 N It is plucked at a point situated at 25 cm from one end. The stretchered string would vibrate with a frequency of

Moderate

A

400Hz
B

100 Hz
C

200 Hz
D

256 Hz

Solution

$n = \frac{p}{2 I} \sqrt{(\frac{T}{m})} F u n d a m e n t a l f r e q u e n c y n, i s g i v e n b y n_{1} = \frac{1}{2 \times 1} {[\frac{20}{5 \times 10^{- 4}}]}^{1 / 2} = 100 H z W h e n t h e w i r e i s p l u c k e d a t 25 c m, i t w i l l v i b r a t e i n t w o s e g m e n t s ∴ Frequency n_{2} = 2 n_{1} = 200 H z$

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