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String Fixed at Both Ends

A string of l...

Question

A string of length 2 m is fixed at both ends. If this string vibrates in its fourth normal mode with a frequency of 500 It's then the waves would travel on it with a velocity of:

A

125 m/s

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B

250 m/s

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C

500 m/s

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D

1000 m/s

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Solution

The correct option is C 500 m/s
$(c)$ For string $λ = \frac{2 l}{p}$
where $p =$ No. of loops $=$ Order of vibrationHence for forth mode $p = 4 \Rightarrow λ = \frac{l}{2}$
Hence $v = n λ = 500 \times \frac{2}{2} = 500 m / s$

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