A stretched string fixed at both ends is set into vibration so that seven nodes (including the two at the ends) are observed along its length.
(i) Identify the harmonic number corresponding to this pattern and state the number of antinodes present.
(ii) Derive a general expression for the wavelength of the nth harmonic in terms of the string length L.
(iii) If the wave speed on the string is 180ms−1 and the length of the string is 0.90m, calculate the frequency of the vibration described in part (i).