Home
Class 11
PHYSICS
(i) A wire is stretched between two rigi...

(i) A wire is stretched between two rigid supports. It is observed that the wire resonates at a frequency of `420` Hz. If a wooden bridge is placed at the midpoint of the wire (so that the midpoint becomes a node), it was observed that the smallest frequency at which the wire resonates is `420` Hz. Find the smallest frequency at which the wire will resonate when there is no wooden bridge.
(ii) A string of length `L` is fixed at one end and is under tension due to a weight hanging from the other end, as shown in the figure. The point of the string on the pulley behaves as a fixed point. Coordinate axes are chosen so that the horizontal segment of the string runs from `x = – L // 2` to `x = L // 2`. The string is vibrating at one of its resonant frequencies with transverse displacement `(y)` given by
`y(x,t) = 0.05 cos(12.0x) sin(360t)`
with x, y in meter and t in second. Write two smallest possible values of L consistent with the given equation?

Promotional Banner

Similar Questions

Explore conceptually related problems

A wire having a linear density of 0.05 g//cm is stretched between two rigid supports with a tension of 450N. It is observed that the wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. Find the length of the wire.

A wire having a linear density of 0.05 g//cm is stretched between two rigid supports with a tension of 450N. It is observed that the wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. Find the length of the wire.

A wire having a linear density of 0.05 g//cm is stretched between two rigid supports with a tension of 450N . It is observed that the wire resonates at a frequency of 420 Hz . The next higher frequency at which the same wire resonates is 490 Hz . Find the length of the wire.

A wire with mass per unit length 0.05 gcm^-1 is stretched between two rigid supports with tension of 4.5xx(10)^7 dynes.it is observed that the wire resonates at a frequency of 420 Hz.The next frequency at which the wire resonates is 492 Hz.Find the length of the wire.

A wire having a linear density of 0.05 kg/m is stretched between two rigid supports. The tension in the wire is 4.5xx10^7 dyne . If the observed that the wire resonates at a frequency of 420 Hz and the next higher frequency at which the wire resonates is 490 Hz, then the length of the wire would be

A wire having a linear density of 0.05 gm/ cm is stretched between two rigid supports with a tension of 4.5 xx 10^(7) dynes. It is observed that the wire resonates at a frequency of 420 cycles /sec. the next resonation frequency at which the same wire resonates is 490 cycles/ sec . the length of wire is approximately.

A steel wire of length 1m is stretched between two rigid supports. The wire is vibrating in its fundamental mode with a frequency 100 Hz. The maximum acceleration at the mid point of the wire is 986 m//s^2 . Then the amplitude of vibration at the midpoint is

A wire having a linear density of 10^(-3) kg/m is stretched between two rigid supports. The tension in the wire is 25.6N . If the observed that the wire resonates at a frequency of 480 Hz and the next harmonic is found to be 640 Hz, then the length of the wire will be

A wire having a linear mass density 5.0 xx 10^(-3) kg//m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. Find the length of the wire.

A wire having a linear mass density 5.0 xx 10^(-3) kg//m is stretched between two rigid supports with a tension of 450 N. The wire resonates at a frequency of 420 Hz. The next higher frequency at which the same wire resonates is 490 Hz. Find the length of the wire.