Using a similar apparatus, a student finds that she must increase the frequency

Question

Using a similar apparatus, a student finds that she must increase the frequency of the source creating the waves by 150 Hz in order to go from a standing wave with 4 antinodes to a standing wave with 5 antinodes.

Now suppose the student doubles the mass of the hanging cylinder and repeats the experiment. How, if at all, will the results be different? That is, would the frequency difference to go from 4 to 5 antinodes be 150 Hz? If not, would the new frequency difference be larger or smaller than 150 Hz? Would it be twice as large or small? Explain your reasoning.

Explanation / Answer

f5 - f4 = 150 hz

5*f - 4*f = 150


f = 150 hz (fundamental frequency)


we know, f = v/(2*L)

and v = sqrt(m*g/d) (here d is linear mass density)

if mass becomes two times v becomes sqrt(2) times.

and f becomes sqrt(2) times.


so, f5 - f4 = f*sqrt(2) = 150*1.414 = 212.132 Hz

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