Question

A 75 cm string fixed at both
ends produces resonant
frequencies 384 Hz and 288
Hz without there being any
other resonant frequency
between these two. Wave
speed for the string is​

Answer 1

Answer:

A 75 cm string fixed at both ends produces resonant frequencies 384Hz and 288Hz without there being any other resonant frequency between these two, wave speed of the string is (a) 144m/s (b) 216m/s (c) 108m/s (d) 72m/s

Explanation:

Answer 2

Answer:

Given,

f1 = 384Hz

f2 = 288Hz

1 = 75cm

change in frequency, Δf = f1 - f2

Δf = 384 - 288

Δf = 96 × 4 - 96 × 3 = 96Hz

The fundamental frequency is f0 = 96Hz

We know that for fundamental frequency the distance between two consecutive nodes i.e. two points where the string is connected (in this case) is equal to half of wavelength

So, λ/2 = 0.75

λ = 2 × 0.75 = 1.5m

Wave speed of the string will be

v = f0λ = 96 × 1.5 = 144m/s

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