First slide

Stationary waves

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 Hz then the waves would travel on its with a velocity of

Moderate

A

125 m/s
B

250 m/s
C

500 m/s
D

1000 m/s

Solution

For string $λ = \frac{2 l}{p}$
where p = No. of loops = Order of vibration
Hence for forth mode p = 4 $\Rightarrow λ = \frac{l}{2}$
Hence $v = nλ = 500 \times \frac{2}{2} = 500 m/s$

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