## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

(a) There will be eight antinodes. (b) The new frequency is $2 f_0$
(a) The standing wave shows 4 antinodes, so the figure shows the fourth harmonic. If the frequency is doubled, then this will be the eight harmonic, which has eight antinodes. (b) $v \propto \sqrt{T}$ If the tension $T$ increases by a factor of four, then the speed increases by a factor of 2. We know that $f = \frac{v}{\lambda}$. If the speed doubles while the wavelength remains the same, then the frequency must also double. The new frequency is $2 f_0$.