A string is stretched between two supports that are L = 1.2 m apart. It resonate

Question

A string is stretched between two supports that are L = 1.2 m apart. It resonates at a frequency of f = 450 Hz with a standing wave pattern that has two nodes between the two supports.

(a) Using the unit of m , find the wavelength l.

(b) (b) Suppose that the tension, T, in the string is increased by a factor of 4. What is the new frequency, f', in unit of Hz , if the string vibrates with the same standing wave pattern that it began with (i.e. A standing wave pattern that has two nodes between the supports).

Explanation / Answer

the wavelenth is ? = L = 1.2m frequency is f = 450 Hz ? & f are related by the equation v = ?f where v is the velocity of the wave also the velocity of a standing wave on a string with density d (ie mass per length ) under tension T is v = v(T/d) so ?f = v(T/d) gives f = v(T/d?²) relates the frequency and the tension it's given that the wavelength remains constant so ?' = ? the increased tension is T' = 4T so the new frequency will be f' = v(T'/d?'²) = v(4T/d?²) = 2v(T/d?²) = 2f so the frequency doubles f' = 2f = 2*450 = 900Hz

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