Question

Three resonant frequencies of string with both ends rigid are 90, 150 and 210 Hz. If the length of the string is 80 cm, what is the speed of the transverse wave in the string?

• A. 45 m/s
• B. 75 m/s
• C. 48 m/s
• D. 80 m/s

Answer 1

The correct option is C 48 m/s

Since the string is fixed at both the ends,

$\frac{n}{2}\lambda =0.8$

$\lambda =\frac{1.6}{n}$

$v=f\lambda =\frac{1.6f}{n}$

$n=\frac{1.6f}{v}$

n must be an integer for every given value of f. Hence,

$n=\frac{144}{v}$, $m=\frac{240}{v}$, $l=\frac{336}{v}$

$v=48m/s$ causes all l, m and n to be integers.