Question

An 80-cm-long steel string with a linear density of 1.0 g/m is under 200 N tension. It is plucked and vibrates at its fundamental frequency. What is the wavelength of the sound wave that reaches your ear in a 20°C room?

Answer 1

Wavelength of the sound wave that reaches your ear is 1.15 m

Step-by-step explanation:

The speed of the wave in string is

`v=\sqrt{(T)/(\mu) }`

where T= 200 N is tension in the string ,
`\mu`=1.0 g/m is the linear mass density

`v=\sqrt{(200)/(1* 10^(-3) )`

`v=447.2 m/s`

Wavelength of the wave in the string is

`\lambda =2L=2* 0.8=1.6 m`

The frequency is

`f=(v)/(\lambda) \\f=(447.2)/(1.6)\\f=298.25 Hz`

The required wavelength pf the sound wave that reaches the ear is( take velocity of air v=344 m/s)

`\lambda=(v_(air))/(f) \\\lambda=(344)/(298.25) \\\lambda=1.15 m`