A $660 H z$ tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is $220 m s^{- 1}$ and the string vibrates in three loops. Find the length of the string.

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Solution

Step 1: Given data
Frequency of the tuning fork, $f = 660 H z$
Speed of the wave on the string, $v = 220 m s^{- 1}$
Step 2: Find the wave length of the wave
Wave length of the wave, $λ = v / f = 220 m s^{- 1} / 660 H z = (1 / 3) m$
Step 3: Find the length of the string
Number of loops, $n = 3$
Therefore, length of the string, $L = (n λ) / 2 = (3 / 2) x (1 / 3) = 1 / 2 m = 50 c m$
Hence. the length of the string is $50 c m$ .

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A 660Hz tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is 220ms-1and the string vibrates in three loops. Find the length of the string.

A $660 H z$ tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is $220 m s^{- 1}$ and the string vibrates in three loops. Find the length of the string.