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  • Wave lengths of two nodes in air are a third note of a fixed frequency. The velocity of sound in air   Option: 1 375 m/s<b

Wave lengths of two nodes in air are a third note of a fixed frequency. The velocity of sound in air 
 

Option: 1

375 m/s


Option: 2

400 m/s


Option: 3

360 m/s


Option: 4

200 m/s


Answers (1)

best_answer

Given , \lambda_1=\frac{90}{175} \mathrm{~m}  and   \lambda_2=\frac{90}{173} \mathrm{~m}

let  f_1 \& f_2  be the corresponding frequencies and V be the velocity of sound in air

V=\lambda_1 f_1 \\

V =\lambda_2 f_2 \\

\therefore f_1 =\frac{V}{\lambda_1} \text { and } f_2=\frac{V}{\lambda_2}

since, \quad \lambda_2>\lambda_1 \quad \therefore f_1>f_2

let,  f  be the frequency of third note.

\therefore f_1-f=4 \\

f-f_2=4 \\

\therefore \quad f_1-f_2=8 \\

\frac{V}{\lambda_1}-\frac{V}{\lambda_2}=8 \\

V\left[\frac{175}{90}-\frac{173}{90}\right]=8 \\

V\left[\frac{2}{90}\right]=8 \\

V=360 \mathrm{~m} / \mathrm{s}

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vinayak

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