Length of a sonometer wire between two fixed ends is . If the fundamental frequencies are in the ratio of , then what is the ratio of lengths of these segments of the wire?
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Frequency
A sonometer wire of length is made of steel. The tension in it produces an elastic strain of . What is the fundamental frequency of steel if density and elasticity of steel are and respectively?
Fundamental frequency,
and
Also,
Putting the value of and in . (i) we get,
or,
A sonometer wire supports a load and vibrates in fundamental mode with a tuning fork of frequency . The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to
A stretched wire long is vibrating with its fundamental frequency of . If the length of the wire is decreased to and the tension remains the same. Then the fundamental freuqency of the vibration of the wire will be
1024
572
256
64
A string is stretched between fixed points separated by 75.0 . It is observed to have resonant frequencies of and . There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
Given and
Hence
The lowest resonant frequency is when
Therefore lowest resonant frequency .
The fundamental frequency of an open organ pipe is 300 . The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is , then the length of closed organ pipe is
For open pipe, , where is the fundamental frequency of open pipe.
As freq. of 1st overtone of open pipe freq. of 1st overtone of closed pipe
Two identical strings and made of same material have tension and in them. If their fundamental frequencies are and , respectively, then the ratio is:
2.25
0.44
1.25
1.5
Using ,
where, tension and
.
In the sonometer experiment, a tuning fork of frequency is in resonance with length of the wire when the iron load attached to free end of wire is . If the load is immersed in water, the length of the wire in resonance would be (specific gravity of iron )
constant; Tension decreases by a factor , length decreases by square root of this i.e., 0.77 .
Two identical piano wires kept under the same tension have a fundamental frequency of . The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be
0.02
0.03
0.04
0.01
The length of the wire between two ends of a sonometer is . What should be the positions of two bridges below the wire so that the three segments of the wire have their fundamental frequencies in the ratio of ?
From formula,
[Given: ]
Therefore the positions of two bridges below the wire are and
i.e.,
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