Subjective Type

Three resonant frequency of a string are $$90, 150$$ and $$210 Hz$$. If the length of the string is $$80 cm$$, what would be the speed of a transverse wave on this string?

Solution

The resonant frequencies of a string are
$$f_1 = 90 Hz, f_2 = 150 Hz, f_3 = 120 Hz$$
length of the string is $$l = 80 cm$$
$$\Rightarrow f_1 = (3/2l) v $$ (v = velocity of the wave)
$$\Rightarrow 90 = \{3/(2\times 80) \} \times K$$
$$\Rightarrow K = (90 \times 2 \times 80)/3 = 4800 cm/s= 48 m/s$$

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