#### Question

A wire of length 80 cm has a frequency of 256 Hz. Calculate the length of a similar wire under similar tension, which will have frequency 1024 Hz

#### Solution

Wavelength λ = 80 cm = 0.8 m

Frequency f_{1} = 256 Hz

Frequency f_{2} = 1024 Hz

By the relation,

Speed = Wavelength x Frequency

→ v_{1} = f_{1} x λ_{1}

→ v_{1}= 0.8 x 256

Also, v_{2} = f_{2} x λ_{2}

→ v_{2 }= 1024 x λ_{2}

Since v_{1 }= v_{2}

→ 0.8 x 256 = 1024 x λ_{2}

λ_{2 } = 0.2 m = 20 cm

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Solution A Wire of Length 80 Cm Has a Frequency of 256 Hz. Calculate the Length of a Similar Wire Under Similar Tension, Which Will Have Frequency 1024 Hz Concept: Sound - Reflection of Sound Waves.