The fundamental frequency of a 100 cm long sonometer wire is 330 Hz. Find out the velocity of transverse wave in the wire and the wavelength of the resulting sound waves in air . Given , velocity of sound in air = 330 `m * s ^(-1)` .

Explanation

For fundamental tone in a wire, two nodes are produced at the two ends. So , length of the wire = distance between two consecutive nodes ` = (lambda)/(2)*`
Here, `lambda` = length of the transverse wave .
According to the question,
` (lambda)/(2) = 100 cm = 1 ` m
So, `lambda` = 2 m
`:.` Velocity of transverse wave in the wire, V = frequency `xx` wavelength = `330 xx 2 = 660 m* s^(-1)`
The frequency of the resulting sound waves in air will also be 330 Hz. Velocity of sound waves in air ` = 330 m* s^(-1)` .
`:.` Wavelength of the resulting sound waves in air
` = ("velocity")/("frequency") = (330)/(330) = 1 m ` .