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Answer :
Final Answer:
1. Fundamental frequency (f)= 150 Hz
2. Wavelength (λ) at 210 Hz= 0.64 m
3. Wave speed (v) on the string= 96 m/s
Explanation:
The fundamental frequency (first harmonic) of the string is calculated by taking the average of the given resonant frequencies (210 Hz, 240 Hz, 270 Hz, and 300 Hz). Thus, [tex]\( f = \frac{210 + 240 + 270 + 300}{4} = 150 \)Hz[/tex].
To find the wavelength (λ) at 210 Hz, we can use the formula
[tex]\( f = \frac{v}{λ} \)[/tex], rearranged to [tex]\( λ = \frac{v}{f} \)[/tex] ,given that f- 210Hz and we already know the wave speed (v) on the string is constant, we can calculate
[tex]\( λ = \frac{96}{210} \approx 0.64 \) m[/tex].
The wave speed (v) on the string can be determined by the formula
[tex]\( v = f \times λ \)[/tex]. Using the fundamental frequency (f = 150 Hz) and the wavelength (λ) calculated at 210 Hz, we get [tex]\( v = 150 \times 0.64 \approx 96 \) m/s[/tex].
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