Question

A violin string emits sound of frequency 510 Hz. How far will the sound waves reach when the string completes 250 vibrations ? The speed of sound in air is 340 m/s.​

Answer 1

$\huge\underline\frak{\fbox{AnSwEr :-}}$

$\implies$ 166.7 m

Data : n = 510 Hz, v = 340 m/s,

v = n$\large\sf\lambda$

$\leadsto$ $\large\sf\lambda$ = $\large\sf\frac{v}{n}$ = $\large\sf\frac{340 m/s}{510 Hz}$

$\leadsto$ $\large\sf\frac{2}{3}m$

This, the wavelength, is the distance covered by the sound wave in one vibration of the string.When the string completes 250 vibrations,the distance covered by the sound waves

$\leadsto$ 250 $\large\sf\lambda$

$\leadsto$ 250 x $\large\sf\frac{2}{3}$ = 166.7 m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀OR

The distance covered by sound during 510 vibrations of the string is 340 m. Hence, the distance covered by sound during 250 vibrations of the string

$\leadsto$ $\large\sf\frac{250}{510} x 340$

$\leadsto$ 250 x $\large\sf\frac{2}{3}$

$\implies$ 166.7 m