Question

A certain string, clamped at both ends, vibrates in seven segments (half wavelength loops) at a frequency of 2.40 × 102 Hz. What frequency will cause it to vibrate in four segments?
(a) 89 Hz (c) 274 Hz (e) 420 Hz
(b) 137 Hz (d) 411 Hz

Answer 1

\[240hz=\frac{c}{\lambda}=\frac{300x10^6}{\lambda}\]\[\lambda=1.25x10^6m=\frac{2L}{n}=\frac{2L}{7}\]\[L=4.375x10^6m\]\[\lambda=\frac{2L}{4}=\frac{4.375x10^6m}{2}=2.1875x10^6\]\[f=\frac{300x10^6}{2.1875x10^6}=137.14hz\]
Another (simpler) way to look at it would be:
\[f=n\frac{v}{2L}\]So the number of segments is proportional to the frequency. \[\frac{4}{7}240hz=137.14hz\]

Answer 2

yep thats right ^^^