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A piano wire weighing 6.00 g and having ...

A piano wire weighing 6.00 g and having a length of 90.0 cm emits a fundamental frequency corresponding to the "Middle C" (v = 261.63 Hz). Find the tension in the wire.

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The correct Answer is:
1480N
`l=90cm=0.9m`
`m=(6/90)gm/cm`
`={(6xx10^-3)/(90xx10^2)}kg/m`
`=(6/900)kg/m`
`f=261.63Hz`
`f=1/(2L)sqrt((T/m))`
`rarr `261.63= `1/((2xx0.09))sqrt{(Txx900)/6}`
`rarr 0.18x261.63=sqrt(150T)`
`rarr 150T=(261.63xx0.18)^2`
`rarr T=((261.63xx0.18)^2)/150`
`=1478.52N=1480N`
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HC VERMA-WAVE MOTION AND WAVES ON A STRING-Exercises
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  2. A steel wire of mass 4.0 g and length 80 cm is fixed at the two ends. ...

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  3. A piano wire weighing 6.00 g and having a length of 90.0 cm emits a fu...

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  6. A one-metre long stretched string having a mass of 40 g is attached to...

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  7. A wire, fixed at both ends is seen to vibrate at a resonant frequency ...

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  8. A string, fixed at both ends, vibrates in a resonant mode with a separ...

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  9. A 660 Hz tuning fork sets up vibration in a string clamped at both end...

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  10. A particular guitar wire is 30.0 cm long and vibrates at a frequency o...

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  11. A steel wire fixed at both ends has a fundamental frequency of 200 Hz....

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  12. Three resonant frequencies of a string are 90, 150 and 210 Hz. (a) Fin...

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  13. Two wires are kept tight between the same pair of supports. The tensio...

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  14. A uniform horizontal rod of length 40 cm and mass 1.2 kg is supported ...

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  15. Figure shows an aluminium wire of length 60 cm joined to a steel wire ...

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  16. A string of length L fixed at both ends vibrates in its fundamental mo...

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  17. A 2 m-long string fixed at both ends is set into vibrations in its fir...

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  18. The equation for the vibration of a string, fixed at both ends vibrati...

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  19. The equation of a standing wave, produced on a string fixed at both en...

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  20. A 40 cm wire having a mass of 3.2 g is stretched between two fixed sup...

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