Question

Will a standing wave be formed in a 6.0 m length of stretched string that transmits waves at a speed of 15 m/s if it is driven at
a frequency of:

a) 12 Hz or b) 15 Hz?

Yes for a), no for b)
No for a), yes for b)
No for both a) and b).
Yes for both a) and b).

Answer 1

Solution)

We know,

λ = v/f

Case 1) 12 Hz wave

wavelength =(15 m/s)/(12 Hz) = 1.25 m

So half a wavelength is 0.625 m, and since 6.0 m is not a whole number of half-wavelengths long. Do, NO standing wave will be formed for it.

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For a 15 Hz wave

The wavelength will be (15 m/s)/(15 Hz) = 1 m.

So half a wavelength is 0.5 m, and 6.0 m is a whole number of half wavelengths long. Hence standing wave will be formed for it.

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No for a) and yes for b)

Good luck!:)