Velocity fo wave in a wire fixed at both ends is `70m//s`, Length of the wire can be varied from `2.5` m to `3.5 m`. In how many ways the resonance can be obtained using one tuning fork at a time out of five tuning forks of frequencies `12,19,29,42,55Hz`

Options

A. 5 ways
B. 7 ways
C. 4 ways
D. 9 ways

Answer

A

Explanation

Minimum fundamental of wire
`=(70)/(2l)=(70)/(2xx3.5)=10Hz`
Maximum fundamental frequency of wire
`=(70)/(2xx2.5)=14Hz`
Hence resonance can be obtained for fundamental frequencies between 10 Hz to 14 Hz and there harmonics.
(i) `12Hz=1xx12Hz`. Hence 12 Hz tuning fork shall produce resonance in fundamental mode of frequency 12 Hz.
(ii) 19 Hz does not lie in ranges 10 Hz to 14 Hz and `2xx10Hz` to `2xx14Hz`. Hence 19 Hz tuning fork does not produce resonance.
(iii) 29 Hz does not lie in ranges 10 Hz to 14 Hz, to `2xx10Hz` to `2xx14Hz` and `3xx10Hz` to `3xx14Hz`. Hence 29 Hz tuning fork does not produce resonance.
(iv) `42Hz(3xx14Hz or 4xx10.5Hz)`. Hence 42 Hz tuning fork can produce resonance in 2 ways.
(v) `55Hz=4xx13.75Hz=5xx11Hz.` Hence 55 Hz tuning fork can produce resonance in 2 ways. Hence resonance can be produced in 5 ways.