Physics f chapter 16 #39

Question

A 100 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 degree C room?

Answer 1

The frequency for a vibrating string is

f= sqrt( T/u)/ (2L) where

L - length

T - tension

u - linear density of the string

The sound will travel more slowly in less denser materials, and faster in stiffer ones. The temperature of the air determines the speed of sound propagation. Also since the speed of sound v is related to the wavelength and frequency as

v= l f and

v(Tc) = 331.3 + 0.606 Tc

Tc- temperature in degrees C

we have

l=v/l and finally

l = (331.3 + 0.606 Tc)/f

When computing keep units in the same system by converting 1.0 g/m to 1 x 10-3kg/m and use L=1m not 100 cm