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One end of a horizontal rope is attached...

One end of a horizontal rope is attached to a prong of an electrically driven fork that vibrates at `120 Hz`. The other end passes over a pulley and supports a `1.50 kg` mass. The linear mass density of the rope is `0.0550 kg//m`.
(a) What is the speed of a transverse wave on the rope?
(b) Whatis the wavelength?
How would your answer to parts (a) and (b) change if the mass were increased to `3.00 kg`?

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
(a) `v = sqrt((T)/(mu))= sqrt((mg)/(mu))` …(i)
`= sqrt((1.5 xx 9.8)/(0.055)) = 16.3 m//s`
(b) `lambda = (v)/(f) =(16.3)/(120) =0.136 m`
( c ) From Eq. (i), we can see that `v prop sqrtm`. If `m` is double, then `v` will become `sqrt2` times. Hence, from the relation `lambda = (v)/(f)* lambda` will also become `sqrt2` times. As `f` remains unchanged.
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