Answer:
(a) f = 185 Hz
(b) v = 266.4 m/s
Step-by-step explanation:
(a) The lowest frequency can be calculated by using the following formula for the calculation of the modes (resonant frequencies) in a string:


n: order of the mode
v: velocity of the waves in the string
L: length of the string = 72.0cm = 0.72m
fn: frequency of the n-th mode
With the information about two consecutive modes you can find the lowest resonant frequency. First you find the resonant mode n:

you solve the previous equation for n:

With this information you can calculate the lowest resonant frequency:

b) You have information about two consecutive modes fn, fn-1. Then, you can calculate the velocity of the waves:

fn = 555 Hz
fn-1: 370 Hz
´
hence, the velocityof the waves in the string is 266.4 m/s