Answer to Question #219014 in Classical Mechanics for Bob

Question

1) A tuning fork of frequency 440 Hz is held above a closed air column that is gradually increased in length. The length of the air column that will produce the second resonance position when the speed of sound is 336 m/s is ___m.

2) The speed of sound where a tuning fork of frequency 262 Hz produces the third resonance position above a closed air column that is 1.59 m in length is ___m/s.

3) The speed of sound is 340 m/s where a tuning fork produces the second resonance position above a closed air column that is 49.8 cm in length. The frequency of the tuning fork is ___ Hz.

Answer 1

1)

$\lambda=\frac{2v}{\nu}=1.53~m,$

2)

$v=\frac{\lambda\nu}3=139~\frac ms,$

3)

$\nu=\frac{2v}{\lambda}=1365~Hz.$