The speed of a transverse wave on a string is 160m/s. If the three resonant frequencies of this string respectively are 160Hz, 240Hz and 400Hz, the length of the string is

Options

A. 80 cm
B. 100 cm
C. 160 cm
D. 200 cm

Answer

B

Explanation

Resonanth frequencies are 160, 240 and 400 Hz,
so their simplest radius are 240.400
i.e., `2 : 3: 5`
Hence, 160 is second harmonic
`rArr 160 = (nv)/(2L)`, where n = 2
Substituting n = 2 and v = `160 ms^(-1)`, we get
`L = (2 xx 160)/(2 xx 160) = 1m`
So, string length is 1 m = 100 cm.