## College Physics (4th Edition)

We can rank the strings according to the time it takes a transverse wave pulse to travel from one end to the other, from largest to smallest: $e \gt b = c \gt a \gt d$
We can write an expression for the wave speed along a string: $v = \sqrt{\frac{F}{m/L}} = \sqrt{\frac{F~L}{m}}$ We can find an expression for the time it takes a transverse wave pulse to travel from one end to the other: $t = \frac{L}{v} = \frac{L}{\sqrt{\frac{F~L}{m}}} = \sqrt{\frac{m~L}{F}}$ We can find an expression for the time in each case: (a) $t = \sqrt{\frac{m~L}{F}}$ (b) $t = \sqrt{\frac{m~(2L)}{F}} = \sqrt{2}\times \sqrt{\frac{m~L}{F}}$ (c) $t = \sqrt{\frac{(2m)~L}{F}} = \sqrt{2}\times \sqrt{\frac{m~L}{F}}$ (d) $t = \sqrt{\frac{m~L}{2F}} = \frac{\sqrt{2}}{2}\times \sqrt{\frac{m~L}{F}}$ (e) $t = \sqrt{\frac{(2m)~(2L)}{F}} = 2\times \sqrt{\frac{m~L}{F}}$ We can rank the strings according to the time it takes a transverse wave pulse to travel from one end to the other, from largest to smallest: $e \gt b = c \gt a \gt d$