JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Waves & Sound

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A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz . The length of the string producing a fundamental frequency of 180 Hz will be ____\ cm.

Answer: 60

Solution

For a string fixed at both ends the fundamental frequency is

f = \frac{v}{2 l}

, and since the wave speed is set only by the tension and the mass per unit length it is unchanged, giving

f \propto \frac{1}{l}

. Therefore

\frac{f _{1}}{f _{2}} = \frac{l _{2}}{l _{1}}

, so

l_{2} = l_{1} \frac{f _{1}}{f _{2}} = 90 \times \frac{120}{180}

. The length of the string producing

180 Hz

60 cm

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Integer answer

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