Final answer:
The wavelength of the 6th harmonic of a stretched string fixed at both ends with a length of 160 cm is 53.33 cm.
Step-by-step explanation:
To calculate the wavelength of the 6th harmonic of a stretched string fixed at both ends, we need to use the formula for the wavelength of standing waves on a string. The formula for the nth harmonic on a string of length L is given by:
\[\lambda = \frac{2L}{n}\]
In this case, the length L is 160 cm, and the harmonic number n is 6.
So, the wavelength for the 6th harmonic is:
\[\lambda_6 = \frac{2 \times 160}{6}\]
\[\lambda_6 = \frac{320}{6}\]
\[\lambda_6 = 53.33 \text{ cm}\]
Therefore, the wavelength of the 6th harmonic is 53.33 cm.